Consider the function f(x) = 2x³ − 12x² − 72x + 9 on the interval [−5, 7]. Find the average or mean slope of the function on this interval. -18 08 By the Mean Value Theorem, we know there exists a c in the open interval (-5, 7) such that f'(c) is equal to this mean slope. For this problem, there are two values of c that work. The smaller one is and the larger one is 5.61

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis y = √8-x, 2 ≤ X ≤…

A:

Q: Eliminate the parameter t to find a Cartesian equation in the form x = f(y) for: √x(t) = −3+² -…

A: Therefore, the required answer is x=16−3​y2+89​y−1627​Explanation:Step 1: Step 2: Step 3: Step 4:

Q: Use algebra and the fundamental trigonometric identities. Your answer should be a number or use a…

A:

Q: If f(x) = 7 sin(2x) arcsin(x), find ƒ'(x).

A: f′(x)=14cos(2x)arcsin(x)+1−x2​7sin(2x)​Explanation:Given function is  f(x)=7sin(2x)arcsin(x) We need…

Q: The random variable X has the probability distribution table shown below. x 46810 12 P(X = x) 0.2…

A: The objective of the question is to find the missing values in the probability distribution table…

Q: PLS HELP ASAP ON ALL ASKED QUESTIONS PLS

A: Global maximum at (2.5, 5) of 31 Global minimum at (0, 0) of 21Explanation: Given that, maximum : In…

Q: how did we find 100/3

A:

Q: 11. Compute (fog)(x), (fog)(-2), (go f)(x), and (go f)(-2) for each pair of functions. (a) f(x) = x²…

A: (a) :(f o g)(x)  = 9x2-21x-6(f o g)(-2) = 72(g o f)(x)   = -3x2+9x+14(g o f)(-2) = -16 (b)  :(f o…

Q: 3. (4.4.1 #15) Find the general solution. y" - 3y + 2y = e³ (1 + x)

A:

Q: u × v = (1, 1, 0), ux w = (0, 3, 1), V X W = (2, −1, 1)

A:

Q: Question 2 The graphs of a function f and its derivative f' are shown. Identify each curve and…

A: We have graphs of f and f'We have to identify curve of f and f'

Q: What are the absolute max and min values for the following function: f(x,y) = x3+x2y+2y2 on the…

A: Answer:Absolute maximum value of function = 2Absolutely minimum value of function = 0The detailed…

Q: If [5 - -8 A = [611] 0 " then A- 1 =

A: The objective of the question is to find the value of 'A - 1' given the equation '5 - -8A = 611'.

Q: #14. Given the integral SS² y² cos xdxdy (a) Evaluate it. "(with the given order of integration),…

A: a.)∫12​∫02π​​y2cos(x)dxdy=∫12​[y2sin(x)∣x=0x=2π​​]dy=∫12​[y2sin(2π​)−y2sin0)]dy=∫12​[y2⋅1−y2⋅0]dy=∫1…

Q: I need help with number 17.

A: If you're seeing the number 17 often, it might mean your guardians are trying to tell you something.…

Q: The temperature of a metal plate at the point (x, y) is given as T(x, y), where T(x, y) is measured…

A: To solve for for  T_y(6,4) , we are seeking out the price of trade of temperature with apprehend to…

Q: A construction firm wants to buy a building site and has the choice between three different payment…

A: Since you have at least $67,000 available for a cash payment, option (a) might be initially…

Q: Evaluate the following double integral: x2 SL √x² + ydzdy. 0

A:

Q: Solve the given system of differential equations by systematic elimination. (D+ 1)x+(D1)y = 8 9x+…

A:

Q: PLS HELP ASAP ON ALL ASKED QUESTIONS

A: Therefore, the required answers are a) 117.694561 degreesTo get this in radians, multiply it by…

Q: Use logarithmic differentiation to find the derivative of y with respect to the independent…

A:

Q: Suppose u and v are differentiable functions of x. Use the given values of the functions and their…

A:

Q: Use implicit differentiation to find y' for 5x4y² + In (xy²) = 5 and then compute y' at (1, 1).…

A: After implicit differentiation we have the derivative as follows:…

Q: Problem 1. Prove Theorem 6.14 which is given below. Theorem (Second Derivative Test). Suppose that ƒ…

A: Theorem (Second Derivative Test). Suppose that f:R→R is C3 in a neighborhood of a critical point…

Q: Let g(x,y)=sin(8x+6y). a) Evaluate correctly g(1,−2). Answer: g(1,−2)=________ b) What is the…

A:

Q: Find equations of the following. x² - 2y²+ x² + y = 5, (5,3,-2) (a) the tangent plane (b) the normal…

A: Please refer below page.If you have any doubts please feel free to ask.Explanation:Step 1: Step 2:

Q: 10 9 со 7 6 5 4 3 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 Find the area inside the circle…

A: ​ Area inside the circle x2+y2=10 above the line y=6 is 44.7295​Explanation:Step 1:​Given a region…

Q: classify the following sequences as geometric or arithmetic and find the general expression for the…

A: The objective of this question is to classify the given sequences as either arithmetic or geometric…

Q: Calculus 1 Question. Please help   Thank you

A: Ans : dxdy​=6cos6xExplanation:Explanation:

Q: 5) Find the volume of the solid generated by revolving the triangular region with vertices (0,0),…

A: The objective of this question is to find the volume of the solid generated by revolving a…

Q: principle: $15,000 Interest Rate: 12% Date borrowed:May 12 Date Repaid : September 16 Time:127…

A: The principal amount is P=15000The interest rate is r=12%=0.12Given time is t=127 days.The simple…

Q: Find the value of (fog)' at the given value of x. Assume that f'(3)=6, g'(4) = -5, g(4)=3, and y =…

A: Given data

Q: B. Find the distance between the point A(-2,2,1) and the plane 3x 5y+z = 5. - C. Find the equation…

A:

Q: Əz Əz and at Use the chain rule to find as || 8」8 z = tan (#). u = 7s + 9t, v = 9s - 7t

A: answers are given below.Explanation:

Q: Suppose z x2 sin y, x = 3s² + 312, y = 2st. =

A:

Q: 1 2x STAR -1

A: y(x)=1e2x−1dydx=ddx1e2x−1Using the Chain Ruleddxf(g(x))=f′(g(x))g′(x)Using the power…

Q: A model for the surface area of the human body is given by the function S = f(w, h) = w0.425 0.725,…

A: The required answer is 0.4997Please find the attached file for details...Thank you...Explanation:

Q: Hello Continuing with this problem, shown in the picture, where the parameterization for S was…

A: Hence, the surface area of the parametric curve is 2​πExplanation:Step 1: Step 2:Step 3: Step 4:

Q: The random variable X has the probability distribution table shown as follows. X -2 -1 0 1 2 P(X =…

A: DETAILED SOLUTION IS PROVIDED BELOWExplanation:

Q: y= log (ln 2x) (This function has no y intercept) • Is this function continuous ? Explain

A: Given function is log(ln2x).

Q: The function f(x)- is concave down on which interval?

A: The function f(x) is concave up on the interval I if f"(x) >0 for all x in I.The function f(x) is…

Q: In (x + √√x². Find the first partial derivatives of the function f(x, y) = ln(x+ 1. fx(-3,4)= 2. fx…

A:

Q: Find the slope of the curve at the given point P and an equation of the tangent line at P. y=x²+5x,…

A:

Q: Match the graph of each function in A through D with the graph of its contour map in 1 through 4…

A: Close together contours indicate a steep slope, wall or cliff..

Q: Find the exact value of each expression. (a) sin 75° sin 5° = 0 (b) cos 105° - cos 15° = 0

A: Formulas are used for solving this problem:-

Q: what is the volume of the solid formed by revolving y = 13sinx*cosx between x=0 to x=pi/2

A: Answer written in explanation Explanation:Step 1: Step 2: Step 3: Step 4:

Q: × Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A: ⟨−22​​,22​​⟩ 42​ Explanation:Given the function,f(x,y)=xy2​,(2,4) Let us solve for the gradient of…

Q: ← The position of a particle in space at time t is r(t) as shown below. Find the particle's velocity…

A:

Q: The Parametric equation of the line that passes through the point A(1, -1, 1) and parallel to the…

A: Given that line passes through the point A(1,−1,1) and parallel to vector v→(1,0,1)To find:…

Q: ns; (fog)(x) = F(x) or (go f)(x) = F(x) Refer to the graphs of the functions f, g, and h to compute…

A: a.f[g(3)]=1b.g[f(3)]=−3c.f[h(3)]=−1d.(h∘g)(2)=2e.h{f[g(3)]}=2f.(g∘f∘h∘f)(2)=−3Explanation:Given the…