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Calc tangent problem

  • #1

Homework Statement


Let f(x)=a(7-x^2)
find in terms of a, the equations of the lines tangent to these curves at x=-1.

Homework Equations


?

The Attempt at a Solution


So I took the derivative of f(x).
f'(x)=a(-2x)+7-x^2
then i plugged in -1 into f'(x)
and i got f'(-1)=2ax+7+1=2ax+8
but the answer to the problem is y=2ax+8a.
I dont know where I went wrong.
 

Answers and Replies

  • #2
Cyosis
Homework Helper
1,495
0
It went wrong at the part where you took the derivative. Write out the brackets and then ask yourself what's [tex]\frac{d7a}{dx}, \frac{-dx^2}{dx}[/tex].
 
  • #3
dx
Homework Helper
Gold Member
2,011
18
The derivative of a(7 - x²) is -2ax.

The slope of a line is not enough to determine the equation of the line. If you have the slope, and also its height at a point b, call it c, then the equation of the line will be:

y = c + (x - b)(slope)

Do you recognize this?
 
  • #4
ok
so f'(x)=-2ax which is the slope.
then to get the set of points
you know x=-1,
so f(-1)=8a.
but if you used point slope format
wouldnt you get y-8a=-2ax(x+1) ?
 
  • #5
dx
Homework Helper
Gold Member
2,011
18
Yes, except you have to replace -2ax in your equation with -2a(-1) since you want the slope at -1.
 
  • #6
o ok.
but wouldnt you still get y-8a=2a(x+1)
which is y=2ax+10a?
 
  • #7
dx
Homework Helper
Gold Member
2,011
18
You calculated f(-1) wrong. It should be 6a not 8a.
 
  • #8
thanks!
 
  • #9
dx
Homework Helper
Gold Member
2,011
18
No problem. :smile:
 

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