1. ## Can someone check my answers

let f(x)= a(7-x^2) for everywhere a doesn't equal x

A) find, in terms of a, the equations of the lines tangent to these curves at x=-1.
so i took the derivative of the function and got f'(x)=-2ax and f'(1)=2a
i then plugged -1 into the original equation and got f(-1)=6a. so i used point slope formula and slope intercept to get the function of the tangent line to be y=2ax+8a

B) find, in terms of a, the y intercepts of the tangent lines at x=-1
i found the y int by letting x=0 and solving for y
so i had y=2a(0)+8a and got y int=8a

C) find the x intercept of the tangent lines at x=-1
i did this by letting y equal o and solving for x
so i had 0=2ax+8a and got x int=-48

I triend checking this on my calculator by putting in a constant for a, i think i'm good with a and b but unsure if my c came out correctly

also, the questions say the y intercepts of the tangent lines, however I only got one tangent line at x=-1, am i right or wrong about this?

2. Originally Posted by rawkstar
let f(x)= a(7-x^2) for everywhere a doesn't equal x

A) find, in terms of a, the equations of the lines tangent to these curves at x=-1.
so i took the derivative of the function and got f'(x)=-2ax and f'(1)=2a
i then plugged -1 into the original equation and got f(-1)=6a. so i used point slope formula and slope intercept to get the function of the tangent line to be y=2ax+8a

Very well done..though you meant $\displaystyle f'(-1)=2a$

B) find, in terms of a, the y intercepts of the tangent lines at x=-1
i found the y int by letting x=0 and solving for y
so i had y=2a(0)+8a and got y int=8a

C) find the x intercept of the tangent lines at x=-1
i did this by letting y equal o and solving for x
so i had 0=2ax+8a and got x int=-48

Why?? $\displaystyle 0=2ax+8a\Longrightarrow\,2ax=-8a\,\Longrightarrow\,x=-4$ , unless $\displaystyle a=0$ , but then the function is zero and all the rest is zero, too

I triend checking this on my calculator by putting in a constant for a, i think i'm good with a and b but unsure if my c came out correctly

also, the questions say the y intercepts of the tangent lines, however I only got one tangent line at x=-1, am i right or wrong about this?
Yes, all the time you talk about "tangent lineS" when it must be clear it's ONE tangent line, at most, at any given point. Nevertheless, perhaps they meant to find the intercepts of ALL the possible tangent lines for ALL the possible values of a, but this only has meaning for the x-inter. which is always the same no matter what the value of a is.

Tonio