Showing increasing or decreasing

[kathrynag]

Homework Statement

Is f increasing or decreasing on f(x)=2x^3+3x^2-36x+5 on [-1,1]

Homework Equations

The Attempt at a Solution

f'(x)<0 for all x in (a,b), then x,y and x, y in [a,b] implies f(x)>f(y) and f is decreasing

 

[Mark44]

So put that idea together with the function you are given. Where is f' > 0? Where is f' < 0? Be sure to consider the domain you're given.

 

[kathrynag]

Ok that makes sense

 

[NoMoreExams]

If you are allowed to use derivatives then I would evaluate f(-1) = 42 and f(1) = -26 so it would appear that it's decreasing but we need to check if there are any critical points in [-1, 1]. So let's evaluate the derivative and we get $$f'(x) = 6x^{2} + 6x - 36$$ so if we set it equal to 0 we get x = -3, 2 both of which are not in our domain so I would think we are done.