## anonymous one year ago Help please?

1. anonymous

3 turning points, should be interesting!

2. anonymous

I have no idea how to start it. Should I derive it first and then find the values?

3. anonymous

I got 0 and -3

4. anonymous

@mukushla was right, f'(x)=0 at the turning point

5. anonymous

@DanJS

6. DanJS

can you find $\frac{ d }{ dx }f(x)$

7. DanJS

that expression will give you the slope of any tangent line to the curve at a point

8. anonymous

When I derive it I got 6x^2+12x

9. DanJS

You just have to remember, $\frac{ d }{ dx }[x^n]= n*x ^{n-1}$

10. DanJS

right, now set that slope expression to what they want, zero

11. DanJS

horizontal line, zero slope

12. anonymous

Dan the man!

13. DanJS

(6x)(x+2) = 0 x can be 2 values , each quantity zero

14. anonymous

Factors right?

15. DanJS

6x=0 or x+2=0 horizontal tangent line

16. DanJS

use those x values in the original f(x) and find out each corresponding y value (x,y)

17. DanJS

or nvermind, they dont want it

18. anonymous

You get all 3 values Dan?

19. DanJS

it is a cubic function , it turns around 2 times,

20. anonymous

So it would be -2 and 0?

21. DanJS
22. DanJS

right

23. DanJS

Take first derivative, set that expression to zero, solve for the values of x for each tangent line if they exist

24. anonymous

Alright thank you so much!

25. DanJS

np

26. anonymous

as usual, well done @DanJS