## anonymous one year ago A. Find the derivative of f at x. That is, find f'(x). B. Find the slope of the tangent line to the graph of f at each of the two values of x given to the right of the function f(x)=x^2-8; x=-1, x=3

1. anonymous

@ganeshie8

2. misty1212

HI!!

3. anonymous

Hey

4. misty1212

you know the derivative of $$x^2$$?

5. misty1212

if the answer is "no" that is fine, i will tell you

6. anonymous

is it 2x?

7. misty1212

yes

8. misty1212

and the derivative of a constant is zero, making the derivative of $$f(x)=x^2-8$$ the function $f'(x)=2x$ that is all

9. anonymous

but its two parts to the question is 2x the answer to them both

10. anonymous

@misty1212

11. misty1212

no $$2x$$ is the derivative you now need the equation for two lines, one where $$x=-1$$ and the other where $$x=-3$$

12. anonymous

f(x)=-1^2-8 and f(x)=-3^2-8

13. misty1212

if $$x=-1$$ then $$y=(-1)^2-8=-7$$ so the point is $$(-1,-7)$$ and the slope is $$2\times -1=-2$$ use the point slope formula to get the equation of the line

14. misty1212

if $$x=3$$ then $$y=3^2-8=1$$ the point is $$(3,1)$$ and the slope is $$2\times 3=6$$ points slope again

15. anonymous

y-(-7)=-2(x-(-1)) and y-(1)=6(x-(3))

16. anonymous

@misty1212

17. misty1212

you can clean them up a great deal, but yes

18. anonymous

y=-2x+5 y=6x-17

19. anonymous

@misty1212

20. anonymous

o Thank you