Mathematics

Problem

For the function

y=\arctan\bigl(x^{3}-2x\bigr)

, consider its behavior near

x=1

. (a) Calculate

\dfrac{dy}{dx}

. Express your answer in simplest rational form. (b) Determine

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

and simplify completely. (c) Evaluate

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

x=1

. Show all algebraic steps, and state the exact value.