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 f(x) attains a local maximum or minimum. Hint: you can reason about where f'(x) is positive or negative without actually computing the full value of f'(x).

Q: (a) h(x) = x^√√x² +1 (b) f(x) = (3x² - 2x+1)³(x¹ -2r²- 3)² 4 (c) g(x) = (3-4) ¹ 5x+7

A:

Q: Let f(x)=√1+4x f'(3)

A: We know that the derivative of x^n=nx^(n-1)

Q: Let h(x) = f(x) = g(x). If f(x) = 9x² and g(x) = 8x, what is h'(-5)? - Do not include "h' (-5) =" in…

A: SOLUTION-

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

A:

Q: 9. From "First Principles" show that if f(x)= == 2 x²-3' then f'(x) = - 2x (x² - 3)²

A:

Q: Find f'(x) for f(x) = ex²+3x+¹¸

A: Given that f(x)=ex2+3x+1

Q: Suppose, f'(x)=2cosx+ sec x, -7<x<7½, and it is known that f(T) =D4. Find the function f(x). IT

A: Integrating on both sides, we get

Q: Let f(x)=x^4-6x^2+10 solve the following    1. Fine the equation of the tangent line when x=1  2.…

A: Please refer to the image below

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: Suppose that Find f'(x). f'(x) = = f(x+h)-f(x) = 6hx - 4h +8h².

A:

Q: If f(4) = 3 and f '(x) ≥ 3 for 4 ≤ x ≤ 7, how small can f(7) possibly be?

A: We have to find the smallest value of f(7)

Q: Differentiate. f(x) = In f'(x) = X 6

A:

Q: f(x) = (4x² + 3x)² h(x) = 7 (4x³ - 6x²)³ b) d) g(x)=√10x² - 5x y = 1 3/(x ³√(x + + 5)²

A: We have to find out derivative for different functions.

Q: 4. Consider f(x) = 6 + (x+3) ²/³. Find the extrema of this function using the first derivative test.

A: We have to find extrema by first derivative test.

Q: 5. use the four- step procedure to find f'(x) 1 b) f(x)24x 2 a) f(x)

A: Use four-step procedure to find derivative of f(x).