Question

The contentment obtained after drinking $x-$units of a new drink at a trial function is given by the function $C\left(x\right)=2x^3-x^2+7x+2$. If the marginal contentment is defined as rate of change of $C$ with respect to the number of units consumed at an instant, then find the marginal contentment when $4$ units of drink are consumed .

Answer 1

$c\left(x\right)=2x^3-x^2+7x+2$

$\frac{dc}{dx}=6x^2-2x+7$

${\frac{dc}{dx}|}_{x=4}=6(4{)}^2-2\times 4+7=95$