Question

The amount of pollution content added in air in a city due to $x$-diesel vehicles is given by $P\left(x\right)=0.005x^3+0.02x^2+30x$. Find the marginal increase in pollution content when $3$ diesel vehicles are added and write which value is indicated in the above questions.

Answer 1

Given, $P\left(x\right)=0.005x^3+0.02x^2+30x$

Marginal increase in pollution content $=\frac{d\left[P\right(x\left)\right]}{dx}$

Thus $\frac{d\left[P\right(x\left)\right]}{dx}=0.015x^2+0.04x+30$

At $x=3$

$\frac{d\left[P\right(x\left)\right]}{dx}=0.015(3{)}^2+0.04(3)+30$

$\frac{d\left[P\right(xx\left)\right]}{dx}=30.255$