If f '(x) is always increasing, which statement about f(x) must be true?

Question

f is a function that is differentiable for all reals. The value of f '(x) is given for several values of x in the table below. If f '(x) is always increasing, which statement about f(x) must be true?

x: -8,-3 ,0, 3, 8
f '(x)	-4	-2	0	4	5

A) f(x) passes through the origin.

B) f(x) is concave downwards for all x.

C) f(x) has a relative minimum at x = 0.

D) f(x) has a point of inflection at x = 0.

Answer 1

C) f(x) has a relative minimum at x=0

It's U shaped, with bottom of the U at x=0