Determine the real number so that the quadratic polynomial matches both the value and…

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

Problem

Determine the real number

k

so that the quadratic polynomial

p(x)=x^2+kx

matches both the value and the first derivative of

\frac{d}{dx}(\tan^{-1}x)

x=0

Related theory

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

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