Question

Assume f(3)=1 and f ' (3) = 4
Let g(x)=x^2 + f(x)
Find an equation of the line tangent to y=g(x) at x=3

Answer 1

*Bookmark*

Answer 2

what do you mean bookmark?

Answer 3

g(x)=x^2+f(x)
g(3)=3^2+f(3)=10
g'(x)=d(x^2)/dx + f'(x) [ sum rule]
=2x+f'(x)
g'(3)=2(3)+4=10
So can you find the tangent line at (3,g(3))=(3,10) ?

Answer 4

yes, m=10 and I will use the point (3,1)
correct?

Answer 5

since g(3)=10 (also), the point you need is (3,10)

Answer 6

ok I can find it

Answer 7

y-10=10(x-3)
y-10=10x-30
y=10x-20 Tangent line

Answer 8

Am I correct?

Answer 9

Yep!

Answer 10

Thanks!!

Answer 11

You're welcome! :)