Given f^ prime (x)=4x+3 and f(0) = - 9 . Find f(x) .

Question

asked Nov 23, 2023 34.9k views

1 Answer

Alexbtr · Answer 1 · 2023-11-28T17:33:49+0000

The derivative is given as

$f^(\prime)(x)=4x+3$

and f(0)=-9.

To find the function f(x),

Take the integral,

$\begin{gathered} \int dy=\int(4x+3)dx \\ y=(4x^2)/(2)+3x+C \\ y=2x^2+3x+C \\ f(x)=2x^2+3x+C \end{gathered}$

It is given that f(0) = - 9 .

$\begin{gathered} -9=2(0^2)+3(0)+C \\ C=-9 \end{gathered}$

Then the function is determined as

Hence the function f(x) is