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 2021-03-05Answered
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.
Start by finding the slope of f(x). To do this, integrate f'(x). The integral comes out to . Now solve for C by solving , which gives us a C value of , thus the function