# Math Help - f(x) increse or decrease

1. ## f(x) increse or decrease

f(x)= -2x^3 + 5x^2 -3x +1
Is f(x) increasing or decreasing when x=-2???
I think its increasing?
also does the f ' (x) and f '' (x) tell you the same thing about cubic fuctions than quadratic functions?

I think the f ' (x) tells me the gradient of the tangent line and f''(x) tells if the turning point is max or min??

2. Originally Posted by wolfhound
f(x)= -2x^3 + 5x^2 -3x +1
Is f(x) increasing or decreasing when x=-2???
I think its increasing?
also does the f ' (x) and f '' (x) tell you the same thing about cubic fuctions than quadratic functions? f' and f" tell you the same thing about ALL functions. (in most cases)

I think the f ' (x) tells me the gradient of the tangent line and f''(x) tells if the turning point is max or min?? Indeed.
$f'(x)=-6x^2+10x-3$

$f'(-2)=-47$

Since -47 is less than 0, we conclude that $f(x)$ is decreasing at $x=-2$

3. Thanks on another question
f(x)=x^2 -2x -8
it says use the first derivative to find exact turning point of f(x)
so f ' (x)= 2x-2
so x =1?? is this correct
so that means the turning point is (1,-8) and the other roots are (4,0) and (-2,0)?
its seems to cut the yintercept at -6? I thought by looking at the constant -8 it woul cut there..

Thanks

4. Originally Posted by wolfhound
Thanks on another question
f(x)=x^2 -2x -8
it says use the first derivative to find exact turning point of f(x)
so f ' (x)= 2x-2
so x =1?? is this correct yes.
so that means the turning point is (1,-9) and the other roots are (4,0) and (-2,0)? Other roots? These are the only roots to f (real).
its seems to cut the yintercept at -6? I thought by looking at the constant -8 it woul cut there..

Thanks
.

5. How is the turning point(1,-9)?
and not (1,-8)?

6. Originally Posted by wolfhound
How is the turning point(1,-9)?
and not (1,-8)?
$f(1)=(1)^2-2(1)-8=-9$

Therefore, your turning point is the point P=(1,-9)

7. Thanks,never knew I should do that
one more question please should the function cut the y intercept at -8(the constant in the original quadratic)

8. Originally Posted by wolfhound
Thanks,never knew I should do that
one more question please should the function cut the y intercept at -8(the constant in the original quadratic) yes. The y-intercept is (0,-8)
.

9. Thanks Dude!