52. Consider the function k given by k(x) = 2|x + 5|. a) For what x-value(s) is this function not differentiable? b) Evaluate k'(-10), k'(-7), k'(-2), and k'(0).

Q: 53. Is the function given by Sx + 1, for x << 4, f(x) -x + 7, for x 2 4, continuous at x = 4? Why or…

A: Given a function, f(x)=x2+1,      for x&lt;4-x+7,     for x≥4 To find whether the function is…

Q: 67. Is the function given by g(x) 1 continuous over %3D x + 5 the interval (-4, 4)? Why or why not?

A: g(x)=1x+5

Q: 9) Determine the third derivative with respect to x for y = In x 10) Given f(x) 2x + 1 and f(1) 4.…

A: Find the derivative

Q: 5. Show that the function f(x)= 3x-9 is not differentiable at x=3. Find the formula for f'(x).

A: To Prove: Show that, given function is not differentiable at x = 3.…

Q: 5. By considering the derivative of the function f : [-1,-1] → R defined by f(x) = show that f-¹…

A: Concept: inverse function: An inverse function, sometimes known as an anti function, is a function…

Q: 4. Find the local maximum and minimum values of f, using both the First and the Second Derivative…

A: The given function is fx=x2x-1. Compute the critical points as follows.…

Q: 2. Find all x values on the graph of f (x) where the tangent line is horizontal for each of the…

A: To find: The values of x on the graph f(x) where the tangent line is horizontal. Given information:…

Q: 2) Given: f(x) = x+sin(2x) over the interval (0,7) a) Use a sign analysis to find the relative…

A:

Q: 64 Use the first derivative test to answer the following: the function f(x) = 49x + I and a local…

A:

Q: 57. Is the function given by Sx + 1, for x 4, g(x) = continuous at x = 4? Why or why not?

A: gx=12x+1,   for  x&lt;4-x+7,   for  x&gt;4 Now left hand limit at x=4 is, limx→4-fx=limx→4-12x+1…

Q: Find a nonzero value for the constant k that makes the function tan(kx) f(x) = 3 3x + 2k2,…

A: Given: f(x)=tan(kx)x,   x&lt;03x+2k2,   x≥0 A function f(x) is continuous at x=a, if limx→a-f(x) =…

Q: Suppose that f is a differentiable function with f(2)=5. If the tangent line to the graph of y= f(x)…

A:

Q: II. Compute the right-hand and the left-hand derivatives as limits to show that the following…

A: Given,

Q: 47. Determine the first and second derivatives of the function f(x) tan" (x² – x +1) tan %3D at x=1…

A: Given: The function, fx=tan-1x2-x+1   To determine: The first and second derivatives of the given…

Q: for x 2 - X Is differentiable at x = 2 but not at x = 1.

A:

Q: 66. What will be the function g(x) resulting from normalizing the function f(x) = x³ − x4 defined in…

A: To find : function gx resulting from normalizing the function fx=x3-x4 defined in the domain 0, 34

Q: 10. Find a function f such that f'(x) =r' and the line 4x - ļy = 3 is tangent to the graph of f. %3D

A:

Q: 9.) f(x) = (2x + 1)* %3D

A: The integration technique to calculate the first derivative is:∫(ax+b)n-1…

Q: 56. Is the function given by Sx + 1, for x 4, G(x) = continuous at x = 4? Why or why not?

A: As we know that  Function will be continuous at x=a if limx→a-fx=limx→a+fx=fa

Q: Determine the extreme values of the function (exact coordinate(s) f(x) = 2sinx – x on the interval x…

A:

Q: 4. For what values of x does the graph of f have a horizontal tangent if f(x) = V3 x – 2 sin(x).

A:

Q: 13. Determine where the graph of the function f (x) = sin(9x) is concave upward and where it is…

A: Given fx=sin9x  ,0≤x≤2π9

Q: Find the absolute maximum and absolute minimum of the function on the given interval. f(x) = x – In…

A:

Q: 1 5. By using the cubic approximation of f(x) = --1 around a = 0 in question 4, estimate the error…

A:

Q: 10. The line y = 5x – 5 is tangent to the graph of f (x) = (x + k)(x² – x) at the point where x = 1.…

A:

Q: 9. Is the function defined by gon3 – 3 if 2. continuous at r= 2? differentiable at x = 2?

A:

Q: 3. Use two rectangles of equal width to estimate the area between the graph of f(x) = x + cos(x) and…

A: Solved below.

Q: 6. Prove if the following function is differentiable y2 = (arctanx + 1)°*

A:

Q: 10. Consider the function f(x, y) = 4 + x* + 3y* a. Show that the Second Derivative Test is…

A: (a) Calculate the value for second partial derivatives w.r.t x and y.…

Q: 1. Identify all the x-values of the candidates for where you might find an absolute maximum or…

A:

Q: Find the value of K that make the function f continuous at x=2 -4 スー3x+2 sin(nx) + kx + k if x 2

A:

Q: 3. Let f be defined by f(x) = e* sin x. What is the slope of the line tangent to the graph of f at x…

A:

Q: #4) Given the function f (x) =x³-x² +2x- 1. Use the second derivative test, where applicable, to…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 8. Find the derivative of the f(x) = ntan x at x = " А. п B. 2 In(1) C. π In (π) D. 2 n In() E. 2n…

A:

Q: At what other point does the tangent line drawn to the curve f (x) = x ^ 3 from (2,8) intersect?

A: Given curve is : f(x)=x3   ..............(1)           and tangent drawn from (2,8)

Q: 5) Use the tangent line at x = 9 to approximate the value of the function f(x)= Vx at x= 8.8.

A:

Q: 5. Consider two entire functions with no zeroes and having a ratio equal to unity at infinity. Use…

A:

Q: 6. Use the limit definition of derivative to find f'(x) for the functions below. (a) f(x) = /4r – 1…

A: limit definition of derivative is f'(x)=limh→0f(x+h)-f(x)h

Q: Find points of discontunity of the function,where k is real number 1 f(x, y) sin(4 – x2 – y?) - -

A:

Q: 4. Find the local maximum and minimum values of f,using both the First and the Second Derivative…

A:

Q: 5. Let f(x) = |cosx),x € (0,21). Determine that where the function S is differentiable, and where it…

A: Since not a particular question asked as per guidelines solution to only first question (i.e Q5) is…

Q: 3. What are is the absolute maximum of f (x) = sin(x) cos(x) on the interval [0, n]?

A:

Q: 2. (a) Demonstrate the method of the limit definition of derivative to find the derivative of f(x) =…

A: Limit of differentiation

Q: defines 2 as y. y- cos (3x2) = 5 a function of x and • differentiate implicity to find az ду

A:

Q: 1) Suppose the second derivative of a contiovous function given by f"(x)=Cx-2 )3 (x-2)2 (sx-) A…

A:

Q: 6. Is the function given by F(x) = at x = 4? Why or why not? 1 x² - 7x + 10 continuous

A:

Q: 7. Use the limit definition of the derivative to find f'(x). Then find the equation of the tangent…

A: