The function is differentiable for

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

Problem

The function g(x)=ln⁡(2x+1)g(x)=\ln(2x+1) is differentiable for x>−12x>-\tfrac12. Which of the following is the equation of the line tangent to the graph of gg at x=1x=1? (a) y=ln⁡3+25(x−1)y=\ln 3+\dfrac{2}{5}(x-1) (b) y=ln⁡3+23(x−1)y=\ln 3+\dfrac{2}{3}(x-1) (c) y=23(x−1)y=\dfrac{2}{3}(x-1) (d) y=ln⁡3+13(x−1)y=\ln 3+\dfrac{1}{3}(x-1)

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