Question

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

a. y= f(x) + g(x)
b. y= f(x) -4g(x)
c. y= 3f(x)

Answer 1

Use this fact:
\[\frac{d}{dx}(af(x)+bg(x))=af'(x)+bg'(x)\]
This is called the superposition principle.