Suppose the curve y=f(x) has a tangent line y=4x−5 at x=1 . Consider the function g(x)=2f(x)+x+1 . What is the slope of the tangent line to g(x) at x=1 ?

Answer 1

Since f'(1)=4 we obtain that g'(1)=2f'(1)+1=8+1=9 so the slope is 9.