Question

Suppose f (x) is a differentiable function defined on the interval [0, 60]. Use the function values given in the table below to answer the following:
x: 0 15 30 45 60
f(x): -3 -1 2 6 2
a) Approximate the value of f '(20).
b) Show that f '(c1) = 1/12 for some value x = c1 in the interval (0, 60).
c) Show that f (c2) = 0 for some value x = c2 in the interval (0, 60).