Find the function f given that the slope of the tangent line at any point (x, f(x)) is f '(x) and that the graph of f passes through the given point. f '(x)=5(2x − 1)^{4}, (1, 9)

Find the function f given that the slope of the tangent line at any point (x, f(x)) is f '(x) and that the graph of f passes through the given point. f '(x)=5(2x − 1)^{4}, (1, 9)

Question
Functions
asked 2021-03-05
Find the function f given that the slope of the tangent line at any point (x, f(x)) is f '(x) and that the graph of f passes through the given point. \(f '(x)=5(2x − 1)^{4}, (1, 9)\)

Answers (1)

2021-03-06

Start by finding the slope of f(x). To do this, integrate f'(x). The integral comes out to \(\frac{(2x-1)^{5}}{2}+C\). Now solve for C by solving \(f(1)=\frac{(2\times1−1)^{5}}{2}+C=9\), which gives us a C value of \(\frac{17}{2}\), thus the function \(f(x)=\frac{(2x−1)^{5}}{2}+\frac{17}{2}\)

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