Answer the following questions about the function whose derivatives are given: (a). What are the critical points? (b). On what interval f is increasing or decreasing? (c). At what points if any does f assume local maximum and local minimum values? (i): f"(x)=(x-1)° (x+ 2), (ii): g'(x) = x(x-1).

Q: (2) Find the derivative of each of the following functions (a) f(x) = (1+x*)²/3 (b) g(x) = V1+…

A: a) We use the power rule and chain rule

Q: A function f satisfies the following conditions. f(-3) = 2, f' (-3) = 0, f(-1) = 5, f' (-1) = 0, f…

A: Given that the function f satisfies the following conditions f(-3) = 2, f'(-3) = 0, f(-1) = 5,…

Q: (x) = (3x + 1)²; (0, 1) (a) Find an equation of the tangent line to the graph of the function at the…

A:

Q: a) Find an equation of the tangent line to the curve. y=f(x)3x2-4x at x = 2. b) Find the derivative…

A:

Q: The graph of f(x) is given below. On what interval(s) is the value of the derivative f'(x) negative?…

A: Given : The graph of the function f(x). To find : On what interval(s) is the the value of the…

Q: Use the first, and second, derivative (given below) to find the intervals of increase/decrease and…

A: Follow step 2 and 3 .

Q: f(x) = x3 + x + 6;    (−2, −4) (a) Find an equation of the tangent line to the graph of the…

A: f(x) = x3 + x + 6Recall the famous rule of differentiation: d(xn) / dx = nxn-1

Q: derivative for this question. I gave the easy function. a) Domain of f(x) is b) Find the…

A: