Chapter 3.1, Problem 5E

In Exercises 1-4, use the definition f'(a) = lim la + h) – f(a) h to find the derivative of the given function at the indicated 1. f(x) = 1/x, a = 2 2. f(x) = x? + 4, a = 1 3. f(x) = 3 – x2, a = -1 In Exercises 5-8, use the definition 4. f(x) = x3 + x, a = 0 %3D f(x) – f(a} x - a f'(a) = lim to find the derivative of the given function at the indicated 5. f(x) = 1/x, a = 2 6. f(x) = x2 + 4, a = 1 %3D 7. f(x) = Vx + 1, a = 3 8. f(x) = 2x + 3, a = -1

In this question, we use derivative rules to compute the derivative of f(x) = 21/2 27/6 a) First express f(x) as in the form ax + cad. Answer: f(2) = b) Write down the derivative rule for the derivative of an expression of the form aa. Answer: FORMATTING: Your answer will contain x and a. c) Compute the derivative of f. Answer: f' (x) =

Find derivative

Which of the following represent the derivative of the function f at the input x = a? Select all that apply. lim An→0 lim b→0 lim Ah→a lim c→a | lim p→0 lim m→a f(a + An) - f(a) Δη f(b) – f(a) b- - a f(a + Ah)-f(a) Ah f(a + c) - f(a) C f(a+p) - f(a) р f(m) - f(a) m - a

The function f(x) is everywhere continuous and differentiable. Prove that if the function f(x) has two real roots, then its derivative f′(x) has at least one root.