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)

Efan Halliday 2021-03-05 Answered
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(2x1)4,(1,9)
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Expert Answer

Derrick
Answered 2021-03-06 Author has 94 answers

Start by finding the slope of f(x). To do this, integrate f'(x). The integral comes out to (2x1)52+C. Now solve for C by solving f(1)=(2×11)52+C=9, which gives us a C value of 172, thus the function f(x)=(2x1)52+172

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