Question

NO WORK PROBLEM: 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.

x –8 –3 0 3 8
f ′(x) –4 –2 0 4 5
If f ′(x) is always increasing, which statement about f(x) must be true?

Answer 1

@Evoker

Answer 2

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

Answer 3

I think this appears to be a problem on relative min, vs relative max, vs point of inflection.

Answer 4

Usually when I am thinking about these problems I use x^2 and -x^2 to remind me about the relationship

Answer 5

I think its relative minimum because there is no change from increasing to decreasing slope or vice versa

Answer 6

I also think relative minimum, since the derivative is 0 and it goes from neg to pos.

Answer 7

Yea, thanks for your input

Answer 8

No problem.