Find the equation of the tangent to the curve of...

Question

Find the equation of the tangent to the curve  of...

colouringme · Answer

$$y = (x ^{2} - 5)^{6}$$ at the point  (2,1)

kainui · Answer

Show your best guess and I'll help you where you're wrong.

colouringme · Answer

I already calculate the m of the curve, the m is -24 , am I correct till this part?
I was thinking of $$m _{1} \times m _{2} = \frac{ 1 }{ 2 }$$

zzr0ck3r · Answer

$y'=6(x^2-5)^5*2x$ so let x = 2 and you get -24
so we know the line looks like y=-24x+b
we use the point to find b
1=-24(2)+b
b = 49
so
y=-24x+49

colouringme · Answer

i'm still confused. Where did the b came from?

zzr0ck3r · Answer

the equation of a line is y=mx+b where m is the slope and b is the value of the y intercept

colouringme · Answer

oohh... sorry for another weird questions ; why do we search for b? why does the m doesn't change?

colouringme · Answer

b is for the equation? but how the m doesn't change?

zzr0ck3r · Answer

I think you might need to go back to algebra book, google slope intercept form of a line.

colouringme · Answer

hmm, okay, thanks for the help though. (:

kainui · Answer

Well if you just have the slope of the line, then that's only part of the equation. But you want the one that's tangent to your line.|dw:1395919304776:dw|