4. If f has a local minimum at x = 0 and a local maximum at x – 2, what can you say about f'(0) and f'(2)? Is there anything else you can say about f'?

Q: 1. Find the general form of f if f'(x) = 4(x).

A: We have to find the general form of the function f if f'x=4 fx. Rewriting the given equation, f'x=4…

Q: Let f (*= {(8) +f(9) for real values of x and y. If f '(0) exist 2 2 and equals –1 and f(0) = 1,…

A: Introduction :

Q: (A) h(x) = 12f(x). %3D h'(2) = %3D (B) h(x) = -119(r). %3D h'(2) = %3D (C) h(x) = 2f(x) + 3g(x).…

A: Given Data: f’(2)=2 g’(2)=-1 (A) h(x)=12f(x) The derivative of the given function. h'x=12f'x For…

Q: Let f(x)=x+(1−x)^(1/2) Find the local maximum and minimum values of f using both the first and…

A: For local maxima or minima:The first derivative test is f'(x) = 0The second derivative test…

Q: 2. Determine f'(1) for the function f(x) = (8x – 6Vx5 + 3) (x² – 9x² +) -

A: A detailed solution is given below

Q: 6. Use the nth derivative test to show that -x has a maximum at x = 0.

A:

Q: 1. Sketch a function f(x) with the following properties: • f'(x) > 0 and f"(x) = 0, for x 2

A: As you posted multiple question , I need to solve only first question.

Q: Let f be a function that is defined and differentiable on all of R. Here is some information about /…

A:

Q: 4. If f(z) is the principal branch of z3, find f'(–1– i).

A:

Q: {(u)= (u² -3)*

A: Given the function is  f(u) = 12u2-32. We have to find f'(u).

Q: 1. Determine f'(x) for each function below: f(x) = x2 – 2x + 3 f(x) = 7x3 · Vx %3D f(x) = x³ In x…

A: As per our company guidelines we are supposed to answer only first three sub-parts. Kindly repost…

Q: 3 Let f(x)= x³ - 2x+: Calculate by definition f'(1). X

A: given function to find the derivative

Q: Find numbers a and b so that f'(1) exists for ax² + b 1 x² f(x) = if if x 1.

A:

Q: A particle moves along the x-axis with position function a (t) = 4 sin for 0 <t< 4n where t is…

A:

Q: Find the following using the table below. X 1 2 3 4 3 4 f(x) 2 1 f'(x) 2 4 3 1 g(x) 2 4 3 1 g'(x) 2…

A: 1) given function h(x)=f(x).g(x)Derivative w.r.t 'x' by using the product ruleformula of the product…

Q: Find the antiderivative F of f that satisfies the given condition F(1) = 2 and specify the domain of…

A:

Q: 9. Given f'(2) does not exist and f"(2) > 0, is x = 2 a maximum, minimum, or neither of f? Explain.

A: Given: x=2f'(2) = does not existf"2&gt;0

Q: 5. Determine f,(x); f(x) = x*², x > 0

A: We need to find out first partial derivative

Q: 4. Consider the graph of a polynomial function below. 2 1 -2 -1 2 4 x -1 -2 a) State the domain and…

A: As you post multiple questions According to guidelines I only solve the first one .

Q: 2. Suppose ƒ'(x) = (x − 1)¹⁰ (x + 2)⁹999 (x + 3)(x + 5)³(x − 2)¹2000. Find all values of x for which…

A:

Q: f'(x) = f"(x) = (x) and (b) Graph f(x), f'(x), and f"(x) with a graphing utility. y 150 -5 100 50…

A:

Q: Ex. 5) For R and Q functions and given that: Q(-1) = 5, R(-1) = -4, R(5) = 7; Q'(-1) =-3, R'(-1) =2,…

A: