The function f(x)=-2x^3+10.2x^2+202.275x+0.87

Question

is increasing on the open interval (?,?).
It is decreasing on the open interval (-oo,?) and the open interval (?,+oo)
The function has a local maximum at ?

I used derivative
-6x^2+20.4x+202.275 and find the root but it doesn't work with this problem.

Answer 1

Yes, it does work,

let's set
-6x^2+20.4x+202.275 = 0
6x^2 - 20.4x - 202.275 = 0
I used the formula and got
x = 7.75 or x = -4.35

remember that the function is increasing when the derivative is postive, and decreasing when ....

so the function is increasing for
-4.35 < x < 7.75
and decreasing for
x < -4.35 OR x > 7.75

You should have a general idea what a function like
f(x) = -2x^3 + ... looks like
so x = 7.75 will produce a local maximum.
Plug x = 7.75 into f(x) to find that local maximum