Let . Which equation gives the normal line to the graph at…

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

Problem

Let y=arctan⁡ ⁣(1+2x)y=\arctan\!\big(\sqrt{1+2x}\big). Which equation gives the normal line to the graph at x=2x=2? (a) y−arctan⁡(5)=165 (x−2)y-\arctan(\sqrt{5})=\dfrac{1}{6\sqrt{5}}\,(x-2) (b) y−arctan⁡(5)=65 (x−2)y-\arctan(\sqrt{5})=6\sqrt{5}\,(x-2) (c) y−arctan⁡(5)=−65 (x−2)y-\arctan(\sqrt{5})=-6\sqrt{5}\,(x-2) (d) y−arctan⁡(5)=−125 (x−2)y-\arctan(\sqrt{5})=-12\sqrt{5}\,(x-2)

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