Question

Find a function f ( x ) such that f ' ( x ) = 8 e x − 4 x and f ( 0 ) = − 5

Answer 1

`f(x)=8e^(x)-2x^(2)-13`

Explanation:

`f^(')(x)=8e^(x)-4x`
On integrating,

`f(x)=8e^(x)-2x^(2)+C`
Since,
`f(0)=-5`

`f(0)=8e^(0)-0+C=-5`

`C=-13`
Hence,

`f(x)=8e^(x)-2x^(2)-13`