Question

F'(x)=2x+17 f(1)=7 what is f(0)

Answer 1

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Answer:

f(0) = -11

Explanation:

The function f(x) is found by integrating its derivative. The constant of integration is found from the given point.

`\displaystyle f(x)=\int{f'(x)}\,dx=\int{(2x+17)}\,dx=x^2+17x+c\\\\f(1)=7=1^2+17\cdot1+c\quad\rightarrow\quad c=-11\\\\f(0)=0^2+17\cdot0-11\\\\\boxed{f(0)=-11}`