The function is defined by for .

MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

The function

g

is defined by

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

for

x\ge -4

. (i) Obtain an explicit formula for

g'(x)

for all

x>-4

. (ii) Evaluate

g'(5)

. (iii) Explain the meaning of the value found in part (ii) with respect to the graph of

y=\sqrt{x+4}

. What does it represent geometrically?

Related theory

Interpreting Derivatives
Advanced Differentiation
Derivatives of standard functions via chain rule
Derivatives of composite functions
Continuity and Differentiability

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