Hello vease1999 Originally Posted by

**vease1999** If f(x) = 4x - e - 0.5 x, and F(x) is an antiderivative function of f(x) with F(0) = 3, which of the following equals F(3) rounded off to two decimal places?

The answer is 19.45

When I worked it out, I got 17.54, which is not right. Could someone explain? Thanks.

I assume you mean:$\displaystyle f(x) = 4x -e^{-0.5x}$

in which case:

$\displaystyle F(x) = 2x^2+2e^{-0.5x}+c$

$\displaystyle F(0) = 2+c = 3$

$\displaystyle \Rightarrow c = 1$

$\displaystyle \Rightarrow F(3) = 18 + 2e^{-1.5}+1$$\displaystyle = 19.45$ (2 d.p.)

Grandad