Find f such that the given conditions are satisfied. f'(x) = x2 + 3, f(0) = 21 f(x) X3 + 3x + 21 3 f(x) = x3 + 3x2 + 21 f(x) = +3 + 3x f(x) = x3 + 3x + 21

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asked Oct 7, 2023 209k views

1 Answer

Lewis Kelsey · Answer 1 · 2023-10-13T16:03:39+0000

We have to find f(x).

First we have to integrate f'(x) and then satisfy the initial condition f(0).

Integrating f'(x):

$f(x)=\int (x^2+3)dx=(x^3)/(3)+3x+C$

We can then replace x with x=0 and f(x) with f(0)=21 to find the value of the constant C:

$\begin{gathered} f(0)=21=(0^3)/(3)+3\cdot0+C \\ C=21 \end{gathered}$

Then, the function f(x) is:

Answer: f(x) = x^3/3 + 3x + 21 (Option A)