Thread: Equation of the line tangent to the curve

I hope this is considered pre-calc...

Here is the question:

Suppose the line tangent to the graph of f at x=2 is y=5x+3 and suppose y=4x-1 is the line tangent to the graph of g at x=2. Find the line tangent to the following curves at x=2.

y=f(x)g(x)

I know the answer for the above is y=87x-83, but can someone show me the steps of the solution to come to that answer? I don't quite understand it. Thanks!

Originally Posted by softwareguy

I hope this is considered pre-calc...

Here is the question:

Suppose the line tangent to the graph of f at x=2 is y=5x+3 and suppose y=4x-1 is the line tangent to the graph of g at x=2. Find the line tangent to the following curves at x=2.

y=f(x)g(x)

I know the answer for the above is y=87x-83, but can someone show me the steps of the solution to come to that answer? I don't quite understand it. Thanks!

y' = f'(x)g(x) + g'(x)f(x)

y'(2) = f'(2)g(2) + g'(2)f(2) = slope of the tangent line to y = f(x)g(x) at x = 2

point of tangency is (2, f(2)g(2))

use the point-slope form to find the tangent line equation