Mathematics

Problem

Let

g(x)=\int_{1}^{x}\bigl(5t^{3}-4t+7\bigr)\,dt

for all real numbers

x\ge 1

. (a) Calculate

g'(x)

. (b) Evaluate

g'(2)

. (c) Determine the equation of the tangent line to the graph of

g

at the point where

x=2

. Express your answer in point–slope form.