Consider , where and are real constants and…

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

Problem

Consider

y=(ax+b)^{-2}

, where

a

and

b

are real constants and

a\neq0

. (a) Find

\dfrac{d^{2}y}{dx^{2}}

. (b) State the condition under which the graph of

y

is concave upward for all real

x

Related theory

Curve Analysis
Advanced Differentiation
Differentiation Rules
Derivatives of standard functions via chain rule
Derivatives of composite functions
Continuity and Differentiability

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