Question

Find f such that the given conditions are satisfiedf’(x)=x-4, f(2)=-1

Answer 1

Given:

`f^(\prime)\left(x\right)=x-4,\text{ and}f\left(2\right)=-1`

To find:

The correct function.

Step-by-step explanation:

Let us consider the function given in option D.

`f(x)=(x^2)/(2)-4x+5`

Differentiating with respect to x we get,

`\begin{gathered} f^(\prime)(x)=(2x)/(2)-4 \\ f^(\prime)(x)=x-4 \end{gathered}`

Substituting x = 2 in the function f(x), we get

`\begin{gathered} f(2)=(2^2)/(2)-4(2)+5 \\ =2-8+5 \\ =-6+5 \\ f(2)=-1 \end{gathered}`

Therefore, the given conditions are satisfied.

So, the function is,

`f(x)=(x^(2))/(2)-4x+5`

Final answer: Option D