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.

x –8 –3 0 3 8
f ′(x) 5 4 0 –2 –4

If f ′(x) is always decreasing, which statement about f(x) must be true?

Answer 1

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

Answer 2

d^2y/dx^2 is -

now let me see if I throw a ball up to the right (x +) at 45 degrees
the slope is + for a while
but it keeps decreasing :)
It is 0 at the top then gets negative