Question

maximum y value
f(x)=-x^2+2x+2
f is increasing x greater than or less than?
f is decreasing x less than or greater to ?

Answer 1

Take the first derivative to find the critical points, where it changes from increasing to decreasing.

f'(x)=-2x+2
-2x+2=0 ---> x=1 Therefore there is a critical point at x=1 (plug into original to find y value. Critical point is at (1,3).

Since -x^2 is an upside down parabola, the maximum is at that point (1,3). As well as that, is must be increasing before that point (-inf,1). and decreasing afterwards (1,inf)

Hopefully this helps. (Might have made a mistake in the algebra, so check it yourself. I am running on 1 hour of sleep :P.)

Answer 2

thanks