Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, en = 8x³ - 12x² - 48x X = f(x)

Q: Suppose F(3) = 2, F(8)= -19, and F"(x) = f(x). —13, and G'(x) = g(x). Also suppose G(3) =0, G(8) = =…

A: use integration  for finding the values.

Q: Suppose f(x, y, z) = x² + y² + 2² and W is the solid cylinder with height 5 and base radius 6 that…

A: Now, the cylinder's base is,

Q: Evaluate the integral: 1. √64 x² 14x² x = 64 tan(0) 64 sec (0) x = 8 sec (0) x = 8 sin(0) x = 64…

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Q: Find f. (Use C for the constant of the first antiderivative and D for the constant of the second…

A: The expression of the second derivative of the function is given byTo determine: The expression of…

Q: An open-top cylindrical container is to have a volume 216 cm³. What dimensions (radius and height)…

A: The objective of this question is to find the dimensions (radius and height) of an open-top…

Q: 37-42. Midpoint Riemann sums Complete the following steps for the given function, interval, and…

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Q: Find the total area of the shaded region bounded by the following curves. x= 12y²-12y³ x=2y²-2y

A: From the given graphRegion is bounded by x=12y2−12y3 and x=2y2−2yFrom the…

Q: K Find all points (x,y) where f(x,y) has a possible relative maximum or minimum. Then, use the…

A: f(x, y) = 5x^2+6xy-3y^2+6x+6y to find local minimum or local max

Q: Let g be the function given by g (x) instantaneous rate of change of gl at x = 1? O O -42 -38 42 38…

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Q: g(b) Use the Substitution Formula, f(g(x))•g'(x) dx = [f(g(x))• g'(x) dx = a. a. 3 S - 3 3 Š - 3 10r…

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Q: Please assist with the steps to solve the problem below.  It is known that the quantity demanded of…

A: It is known that the quantity demanded of a certain make of portable hair dryer is x hundred…

Q: Let {n} and {n} be sequences such that n→ L and yn → M. Prove (using the definition of convergence)…

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Q: The marginal profit, in dollars from drilling a well that is x feet deep is given by P'(x) = x. Find…

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Q: True or false: If f is a differentiable function, then [ƒ(√)] = d dx f'(x) 2√x

A: To determine whether the following statement is true or false.If  is a differentiable function, then…

Q: Given: (x is number of items) Demand function: d(x) = 608.4 -0.5x² Supply function: s(x) = 0.4x²…

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Q: Consider the given limits (a is a constant). lim f(x) = 0 lim g(x) = 0 D+X limp (x) = ∞ limq (x) = ∞…

A: Here we have, limx→af(x)=0limx→ag(x)=0limx→ah(x)=1limx→ap(x)=∞limx→aq(x)=∞

Q: Given the graph ƒ(x), find ³5 f(x) dx using formula(s) from geomet

A: We have to find the integral value.

Q: You are building a closed wooden shed in the shape of a rectangular box with a square base. The shed…

A: You are building a closed wooden shed in the shape of a rectangular box witha square base. The shed…

Q: (b) A cone-shaped ice is melting at the rate of 2 m³/s in a manner that maintains its original…

A: The initial radius is r=50 mThe initial height is h=100 mFind the ratio of height over a radiusThe…

Q: 1 = Is the area between the graph of f(x) and the x- axis over the interval [1, ∞) finite or in…

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Q: Find the volume generated by rotating the region bounded by y= 2 cos(x) and the x-axis and ㅠ 3π…

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Q: Suppose sin(theta) = 3\5 and theta in quadrant 2. Find the exact value of the following. Solve with…

A: Since you have asked multiple sub parts in a single request so we will be answering only first three…

Q: Suppose F(3) = 5, F(6)= −5, and F(x) -5, and F'(x) = f(x). f§ 4 ƒ ( x ) d x =

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. x = (y² + 2)³/2,…

A: The area of the surface of revolution of  rotated about the x-axis on  is:

Q: Find the volume generated by rotating the region bounded by y = 2 cos(x) and the x-axis and ㅠ 3π…

A:

Q: Find the absolute maximum and minimum values of f(x)=10x(2-lnx) on [1,e^2]

A: To find the  absolute maximum and minimum values of .Note: Since, the student has posted multiple…

Q: Consider the function the f(x) = x¹(4 − x)³. (a) Find all critical numbers of f(x). (b) Find the…

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Q: 不 any finus given by the marginal-demand function D'(x)= the D(x)= my of hat con 3000 x² where x is…

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Q: Consider the triangle below (not drawn to scale). A ZA= b ZB= с C Let a = 10, b = 7 and ZC = 150°.…

A: a=10b=7Angle C= 150 degree

Q: For the following function, a) give the coordinates of any critical points and classify each point…

A: Consider the function

Q: (1) The critical values of f(x) = 9x + 16x³ + 6x² + 7 are at x = (A) 0 only (B) -1 and 0 (C) -1 and…

A: To find the critical values of .

Q: Find the relative extreme points of the function, if they exist. Then sketch a graph of the…

A: Consider the function

Q: Suppose sin(theta) = 3\5 and theta in quadrant 2. Find the exact value of the following. Solve with…

A: Given:, where   is in 2nd quadrant.To find:To find the exact value of the following.Note: Since, the…

Q: Use the Mean Value Theorem to prove: If f(x) and g(x) are differentiable on an interval (a, b) and…

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Q: By trial and error, determine the value of log215

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Q: If n is a prime number greater than 3, what is the remainder when n² is divided by 12?

A: The objective of this question is to find the remainder when the square of a prime number greater…

Q: A road perpendicular to a highway leads to a farmhouse located a=1.5 km away.An automobile travels…

A: Consider the situation

Q: Obtain general solution. 1) y''-y=ex-4

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Q: Find all exact solutions on the interval 0 ≤ 0 < 2. If there is more than one answer, enter them as…

A: Given that the equation we have to find the exact solution of the given equation

Q: Differentiate implicitly to find dx x²y-2x³-8=0; (2,6) The slope of the curve at (2,6) is Then find…

A: we are given an implicit function and we need to find out the slope at the given point.

Q: Find the volume V of the solid below the paraboloid z=4-x-y and above the following region.…

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Q: The sum + is between 8 (A) and 3 (B) and 1 (C) 1 and 1 14/ D) 1 and 1/2 E) 1 and 2

A: The given is  Sum of this can be calculated  as           =                         =…

Q: Graph the polynomial P(r) = ³ + ² -5r +3 using calculus by showing the given steps: (a) Find the r-…

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Q: Find two positive numbers that satisfies the given requirements. The product is 147 and the sum of…

A: To find two positive numbers that satisfies the given requirements.The product is 147 and the sum of…

Q: O The system has no solution. O The system has a unique solution. The solution set is. {000}. O The…

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Q: Activity 10.6.5. Consider the function f defined by f(x,y) = =−x + 2xy − y. a. Find the gradient ▼…

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Q: Find the total area of the shaded regions enclosed by y = 3x³ – x² – 11x and y = − x² +> - X.

A: The intersection points are (-2,-6),(0,0),(2,-2)

Q: Suppose you are given a triangle with Then a = degrees, and C = degrees. Enter your answers with two…

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Q: An object's velocity after t seconds is V(t) Enter an integer or a fraction. DO NOT enter decimals.…

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Q: Problem Let g(x) = f f(t) dt, where f is the function whose graph is shown below. Evaluate g(4). 2 1…

A: Consider the graph