Let , where and are differentiable and for all . For to have a horizontal tangent at…

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Let

h(x)=\dfrac{p(x)}{q(x)}

, where

p

and

q

are differentiable and

q(x)\neq0

for all

x

. For

h

to have a horizontal tangent at

x=a

, which of the following conditions must be satisfied? (a)

p'(a)=0

(b)

p'(a)q'(a)=0

(c)

p'(a)q(a)-p(a)q'(a)=0

(d)

p(a)=0

Related theory

Differentiation Rules
Derivatives of standard functions via chain rule

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