Answer the following questions about the function whose derivative is f'(x) = (x - 6)“(x + 9). a. What are the critical points of f? b. On what open intervals is f increasing or decreasing? c. At what points, if any, does f assume local maximum and minimum values? .....

Q: Q1) The dervative of the function f(x)= |x+2, using the definition of derivative is 1 b)- a) x+2 x+2

A:

Q: S(r) = In (r² + 2x + 5)

A: SOLUTION-

Q: Answer the following questions about the function whose derivative is given below. a. What are the…

A: Given :                                                        f'(x) = (√3 sin x - cos x)(sin x + √3…

Q: Let f(x)=1.91.9x. Estimate the derivative f′(1.1) to within two decimal places by using a small…

A: The given function is f(x) = 1.91.9x.

Q: 3. Suppose the function f has second derivative f"(x) = x2(x – 3)(x+2)*(? – 1). = T- (a) How many…

A:

Q: Find the approximate value of derivative f′(0) with the step size h for the following function by…

A:

Q: 4) Calculate the first derivative of the following functions: 1. f(x) = In 2x2+1° 2. f(x) =…

A:

Q: The derivative of the function f is defined by ƒ'(x) = (x² + 1) cos (x²). If f(1) = 1, what is the…

A:

Q: Answer the following questions about the function whose derivative is given below. a. What are the…

A: Given: f'(x)=3sinx-32cosx+1, 0≤x≤2π To find: a) Critical points of f. b) The intervals in which f is…

Q: 4. Use the definition of derivative to compute the derivative of the following functions at x 1: a.…

A:

Q: 9. Suppose for sume funchion f we have its derivative, f'x) = e*sin(x), on the %3D interval o< x<…

A: We can use application of derivative in order to solve the given problem.

Q: Find the critical points of the following function. f(x) = 5x? - 3x – 1 What is the derivative of…

A:

Q: Suppose the function f(x) has the derivative f'6): 4x-122 -8 こい x-) G。 C) what are the x-values of…

A: Here given derivative of function f(x) as f'x=4x-2x+12 (a) To find the critical point of function…

Q: 4. Given f (x )=x'-12x +1. Use the second derivative test to determine the local extremum off (x).

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Suppose that the first derivative of f(x) =- is approximated by the following formula 3x+4 -2f(x –…

A: The given problem is to find the actual error of the first derivative of the function using the…

Q: Find f'(a) using the definition of the derivative at a point for: f(x). 1 = √x at a = 4.

A: Find derivative using  definition of f(x)=1x at a=4

Q: 2. Let f(x) = /1 – x² . Find f(8) (0), i.e., the eighth derivative of ƒ evaluated at the point 0.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Please identify the critical point,z, where the first derivative is equal to zero for the following…

A: Critical point

Q: 3. Estimate the derivative of the function, f(x) = cos x + tan1 x, at xi= 0.5 using Richardson's…

A: To find the derivative of the function fx at x=x0 by Richardson's extrapolation centered finite…

Q: Find the derivative of the following function using the limiting process. f(x) = 1/x2

A:

Q: ) Given the following derivative function 2x – 5 f'(r) = Þ – I^ what are the critical numbers of…

A:

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

A: Given,

Q: Find the derivative at the given point. f(x)= at x = 0 %3D x+1 O 1/4 O-1

A:

Q: Answer the following questions about the function whose derivative is f′​(x)=​x(x+4​). a. What are…

A:

Q: (e) Use a backward finite difference approximation to approximate the first derivative of the…

A:

Q: Suppose that the first derivative of f(x) = x² In x is approximated by the following formula f'(x) ≈…

A:

Q: 2. Given the graph of derivative f'(x), find: a) Any interval (s) where f(x) is decreasing b) Any…

A: the function is decreasing when  as we can see from the graph,  on the interval  and  which means…

Q: Answer the following questions about the function whose derivative is f'(x) = (x- 2) (x+ 8). a. What…

A: Given the derivative of a function: f'x=x-22x+8

Q: Find a positive value, c, for x, thot satisfies the Mean valve Theorem for derivatives for…

A:

Q: Answer the following questions about the function whose derivative is f (x) = x(x- 4). a. What are…

A:

Q: Answer the following questions about the function whose derivative is f' (x) = x(x + 3). a. What are…

A:

Q: Use the first derivative to answer the following questions: What are the critical points of f? Where…

A: Given: f(x)=sinx-cosx      0≤x≤2π

Q: 1 Answer the following questions about the function whose derivative is f'(x) = x a. What are the…

A: For critical points we take f'(x) =0 then solve for x.  If f'(x) &lt;0 then f is decrease.  If f'(x)…

Q: 19.What is the derivative with respect to a of f(x) = 4-32 3z+2 4x-3

A:

Q: 1 Answer the following questions about the function whose derivative is f'(x) = x a. What are the…

A: Given equation of derivative,  f'(x) = x-1/5(x-4)    For part A).  f'(x) = 0 x= 0 and 4 are critical…

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: Find the approximate value of derivative f'(0) with the step size h for the following function by…

A:

Q: 3 Consider the function f(x) = 2+ 1+ (x+1)? Compute the derivative f'(x) . Determine all of the…

A:

Q: Find the critical point and the interval on which the given function is increasing or decreasing,…

A: The given function is fx=9x2+7. Note that, the denominator of the above function is not 0 for any…

Q: In our last class discussion we found that a function y(x)= x* indicated by taking y"(x) = 0 that…

A: Definition: The first derivative of a one-variable function is zero at the points called stationary…

Q: Use backward, forward , and centered difference approximation to estimate the second derivative of…

A:

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: find a linearization at a suitably chosen integer neara at which the given function and its…

A: Consider the following function: fx=x2+2x Differentiate fx with respect to x: ddxfx=ddxx2+2xf'x=2x+2

Q: (e) Use a backward finite difference approximation to approximate the first derivative of the…

A:

Q: f′(x)=(x−3)2(x+6). a. What are the critical points of​ f? b. On what open intervals is f increasing…

A:

Q: Derive the following formula for approximating the derivative f": 1 f"(x) ≈ (-f(x+2h) + 16f (x + h)…

A: Given: The formula is f'(x)≈112h -f(x+2h)+8f(x+h)-8f(x-h)+f(x-2h). To prove: The given formula. To…

Q: 1. Use the following formula (1) to evaluate derivative for each of the functions below: f(x+ h) -…

A:

Q: 8 x - y a(x, y)

A: Given :- The given multivariable function is ax,y = 8x-yex2 +y2. To determine :- The critical points…

Q: Find the approximate value of derivative f'(0) with the step size h for the following function by…

A: