Question

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

Answer 1

Given

The derivative is given as

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

and f(0)=-9.

Step-by-step explanation

To find the function f(x),

`dy=(4x+3)dx`

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

`f(x)=2x^2+3x-9`

Answer

Hence the function f(x) is

`2x^2+3x-9`