Question

What is the equation of the tangent to each curve at this indicated value. f(x) = (x²-3)(x²+1); x=4

Answer 1

Do you know how to find the derivative of the function?

Answer 2

yes, is that all i do ?

Answer 3

Yes, find the derivative and then substitute the x-value you are given to find the slope at x=4. Then just use that as a slope and use it to find the equation of the line.

Answer 4

Ohhh ! thanks :D

Answer 5

Not a problem!

Answer 6

so if m=4 what do i do from there?

Answer 7

The formula for the tangent line of a function \(f(x)\) at the point \((a, f(a))\) is given by:\[
y-f(a) = f'(a)(x-a)
\]

Answer 8

The formula for the tangent line of a function \(f(x)\) at the point \((a, f(a))\) is given by:\[
y-f(a) = f'(a)(x-a)
\]
Given that \(a=4\) and \(f(a)=(16-3)(16+1)\)\[
y-(16-3)(16+1) = f'(4)(x-4)
\]