Let for all .

MATHEMATICS · Multi-part · A Level · Mathematics · Differentiation · Differentiation

Problem

Let

g(x)=\sqrt{4x+1}

for all

x\ge -\dfrac14

. (1) Write an expression for the average rate of change of

g

on the interval

[2,2+h]

, where

h\neq 0

. Simplify your expression as far as algebraically convenient. (2) Determine the instantaneous rate of change of

g

x=2

by evaluating the limit of your expression from part (a) as

h

approaches

0

. Show all algebraic steps leading to your final numerical answer.