Answered: Find the values of constants a, b, and…

Find the values of constants a, b, and c so that the graph of y=ax^3+bx^2+cx has a local maximum at x=-2, a local minimum at x=-4 and inflection point at (-3,18)

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 97E

See similar textbooks

Related questions

Q: Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an…

Q: Construct a polynomial function with the following properties: fifth degree, 2 is a zero of…

A: Degree = 5 2 is a zero of multiplicity 3−2 is the only other zeroleading coefficient is 3.

Q: Given that f(x)=√x-5 and g(x)=x+1, what is the rule and domain for fog)(x) Only one item from the…

Q: Consider the following polynomial function. f(x)=(x+1)2(x−2)5(x−3) Step 2 of 3: Find the…

Q: Current Attempt in Progress Given the figure and [ f(x)d(x) = 1.25, estimate: (a) f f(x) dx = (b) […

A: Given that.We will find the remaining values.

Q: Suppose that your first guess with Newton's method is lucky, in the sense that xo is a root of f(x)…

A: Nweton's method

Q: f(x)= [5x+3] e-2x

Q: Express the limit as an integral. 4 lim (7(x)² - 2(x, ) ³) 4x over [0, 4] n→ ∞o Σ i = 1 dx

Q: 1. y'(t) − y(t) = 1, Ans. y(t) = e' - 1 y(0) = 0

A: given IVP

Q: Find an equation of the tangent to the curve at the point corresponding to the given value of the…

A: To find the slope of the tangent we need to find dy/dxThen find dy/dx at t=pi

Q: Find the x-coordinate of the point on curve y=In(2x²-11x) where the tangent line is horizontal. Just…

Q: - 9 √²x²=2 dx = √² ((x² + 1) = 10) dx 1 + 10 1 +

A: ∫01x2−91+x2dx=∫01((x2+1)−101+x2)dx

Q: Kevin needs to find the length of the arc of the given curve. He is struggling. Please help him by…

A: given curve

Q: 0-5-5 x'(t) = -5 0-5 x(t). x( -5 -5 0

A: We have to solve the given initial value problem.

Q: 1. Evaluate each of the following derivatives. You need not simplify your answer. (a) √t (2-1)³ dt d…

Q: Given the acceleration a= initial velocity, and initial position of a body moving on a coordinate…

A: The given acceleration is.The aim is to find the .

Q: (a) Find the initial population. (Round your answer to the nearest whole number.) X bacteria (b)…

A: The number of bacteria in a culture is increasing according to the law of exponential growth. There…

Q: 17. The velocity graph of a braking car is shown. Use it to estimate the distance traveled by the…

Q: Part III. A tank contains 400 liters of water. A solution with a salt concentration of 0.4 kg/L is…

Q: Suppose that in a memory experiment the rate of memorizing is given by M'(t) = -0.004t² +0.2t, where…

Q: Using the figure below, estimate e 9 30 [²56x) 3 30 60 6 f(x) dx 12 15 f (x) dx. 15 Enter your…

Q: 6) Show that=1

Q: 2. Find the indefinite integrals and check your solutions by differentiating. C √ (3x²-2) dx b) f…

Q: 2. Solve the DE 1. 2. (D-D³-9D²-11D-4)y=0 (D-4D³ +8D²-8D+4)y=0

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: How would I set up an integral that funds the volume of the cylinder?

A: This is question of calculusHere we have to find step for calculate the area of cylinderFurther…

Q: and g(x)=x+9, what is the rule and domain for 7X)? Only one item from the answer bank will be used…

Q: (a) Sketch the graph of r = 8 cos 0 by plotting at least 4 points in polar coordinates. Label the…

A: given a equation

Q: Use the Root Test to determine whether the series convergent or divergent. 5n 2n Σ (-20) ³ n+ 1 n =…

Q: Find a basis for the 2-dimensional solution space of the given differential equation: y" - 5y' = 0

A: The given differential equation is

Q: C. Evaluate d²y dx² at the point (1,2)

A: Consider the curve

Q: 1. Use Elementary Row Reduction and Gauss elimination to solve the following linear systems: { (a).…

Q: fx csc x² c X CSC csc x² cot x² dx

A: +C

Q: Evaluate the trigonometric integral, using a Pythagorean identity. 3 fm (sec (sec²(0) - 7π/6 6√³…

Q: A contractor drew up plans for an addition to a house. The new outside walls will be a total of 80…

A: A contractor drew up plans for an addition to a housse. The new outside walls will be a total of 80…

Q: Evaluate the following integral. Š 12x - 61 dx

Q: At a certain instant in time, the number of cars, N, traveling on a portion of a certain highway can…

A: The objective of the question is to find the estimated number of cars, N, traveling on a 1-mile…

Q: Find the equation of the tangent line to y = (x³ + 2x + 3) eª at the point where x=0. The equation…

Q: The graph of f(x) is shown (see figure). 6x x² + 1 f(x) (a) Find the following limits. lim f(x)= x →…

Q: Graph the function y= by identifying the domain and any symmetries, finding the derivatives y and y…

Q: Σ 8 n=1 (-2)n-1 √n

A: Note:-Since you asked multiple questions, according to our policy we can answer only first question…

Q: Consider the following expressions (a) (b) div(gradf) (c) grad(div f) div(curl(gradƒ)

A: we need to classify the given expression.

Q: (MC) A This is the only question in this section. Question If f (x) = cos x, then the Mean Value…

Q: Consider the curve y = point P(9,0). The closest point is Q(x, y) √4x + 16. Find the point on this…

A: We have given curve

Q: Eliminate the parameter t to find a Cartesian equation in the form x = f(y) for: 4t² = [x(t) = ly(t)…

Q: 8. Describe the domain for h(x) = √70-9x - x²

A: To describe the domain for .

Q: Solve the rational equation. YOU MUST SHOW ALL OF YOUR WORK!

Q: Transform the given system into a single equation of second-order x₁ = −5x₁ + 7x2 x₂ = -7x1 - 5x2.…

A: We have to transform the given system into a single equation of second order.

Q: The graph shows the derivative of a function f. If f(0) = 3, what is f(2)?

A: given graph of the f' to find the value of f(2).

Q: Write (x³ - 3x) dx as the limit of a Riemann sum with intervals of equal width and right endpoints…

A: The given integral is

Q: Let f(x) = x³ - 2x² - 5x + 6. If x = 1 is a zero of f(x), use the Factor Theorem and synthetic…

Question

Find the values of constants a, b, and c so that the graph of y=ax^3+bx^2+cx has a local maximum at x=-2, a local minimum at x=-4 and inflection point at (-3,18)

Formula Formula A function f ( x ) is also said to have attained a local minimum at x = a , if there exists a neighborhood ( a − δ , a + δ ) of a such that, f ( x ) > f ( a ) , ∀ x ∈ ( a − δ , a + δ ) , x ≠ a f ( x ) − f ( a ) > 0 , ∀ x ∈ ( a − δ , a + δ ) , x ≠ a In such a case f ( a ) is called the local minimum value of f ( x ) at x = a .

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1: using all given data.

VIEW

Step 2: Find all constant value

VIEW

Solution

VIEW

Step by step

Solved in 3 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Find the value of x that results in a maximum value of y if -2=x^2+y^2-4x+4y?
Determine the vertex- f( x)= x^2 +4x +3. O (2,-1) O (2,-1) O (3.-1) O (1,-2) MacBook Air F5 F6 F7 F8 &
The graph y= b - (x + a)^2 passes through the points (0, -3), (1,0) and (C,0). Find the value of C.
Calculate the relative minimum and maximum of the following equation f(x) = 8x^3 - 13x^2 - 6x -8 and make the graph.
Find the coordinates of the maximum point of the curve y = x^3 - 12x + 8.
The function f(x)=-2x^3+27x^2-48x+11 has one local minimum and one local maximum.
One of the stationary points of the function y = 4 - 6z +z -2 is (-1,1). Is this a maximum or minimum point of the graph? Answer Next > or press RIG Report feedbackorerror
Consider g(x) = 2x^2-4x-1 A. Determine if the function has maximum and minimum value B. State the maximum or minimum C. State the domain and range
Find a function f whose graph is a parabola with vertex (3, -2) and that passes through the point (4, 5).
Determine where the graph of ?(?) = x^3+x^2-5x-5 is concave up and concavedown and identify inflection points.
The parabola is the graph of a quadratic polynomial p(x) = ax^2 + bx + c. A point (x0, y0) is a point on such parabola if p(x0) = y0; i.e. ax^2 0 + bx0 + c = y0. Find a quadratic polynomial such that the following three points are on the parabola defined by it: (−1, 3), (0, 4), and (1, 2). (Hint: Note that to find p(x)=ax+by+c we need to find numbers a, b and c using three linear equations obtained from given information above).
Graph the function f(x)= -2x^3 + 4x^2 + 2x - 4 Please name any x-intercepts and y-intercepts in the graph Please show all work!!