Question

For a certain function, f'(x)=3+x. For what value of x does the function have a stationary point? What type of stationary point is it?

I've found x to be -3, but how do I determine the type of stationary point?

Answer 1

You know that if f'(x) = 3+x , then
f(x) = 3x + (1/2)x^2+ c
which is a parabola opening <b>upwards</b>, so when x = -3 you have a vertex
and that vertex must be a minimum point.

Answer 2

f'(x)=3+x
you know that f'(-3) = 0
for x < -3, f' < 0
for x > -3, f' > 0
so, f(x) is falling, then stationary, then rising
Looks like a minimum to me.