Question

Calculus help?

Let f be a function that is differentiable everywhere.
The value of f ' (x) is given for several values of x in the table below.
x -10 -5 0 5 10
f'(x) -5 -3 0 2 4

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

f(x) has a relative minimum at x = 0
f(x) is concave downwards for all x
f(x) has a point of inflection at x = 0
f(x) passes through the origin
f(x) is an odd function

Answer 1

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