In each part, find the value of k for which the graphs ofy = f(x) and y = ln x share a

Chapter 3, Problem 42

(choose chapter or problem)

Confirm your result by graphing both \(y=x\) and \(y=\log _{b} x\) in the same coordinate system. In each part, find the value of k for which the graphs of \(y=f(x)\) and \(y=\ln x\) share a common tangent line at their point of intersection. Confirm your result by graphing \(y=f(x)\) and \(y=\ln x\) in the same coordinate system.

(a) \(f(x)=\sqrt{x}+k\)


(b) \(f(x)=k \sqrt{x}\)

Equation Transcription:

Text Transcription:

y=x

y=log_b x

y=f(x)

y=ln x

f(x)=sqrt x+k

f(x)=k sqrt x

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