The curve has a tangent line with slope at exactly one point in the interval

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

The curve

y=\arccos\left(\dfrac{x}{2}\right)

has a tangent line with slope

-1

at exactly one point in the interval

0<x<2

. Determine the coordinates of this point and write the equation of the tangent line.

Related theory

Straight Lines
Advanced Differentiation
Derivatives of standard functions via chain rule
Derivatives of inverse trigonometric functions
Continuity and Differentiability

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