Mathematics

Problem

A differentiable function

f

has a tangent line at

x=1

given by

L(x)=3x+2

. (a) Determine the values of

f(1)

and

f'(1)

. (b) Describe in complete sentences what the slope and

y

–intercept of the tangent line indicate about the local behavior of the graph of

f

near

x=1

. Explain your reasoning without performing any additional calculations.