The amount of pollution content added in air in a city due to x-diesel

1.	The amount of pollution content added in air in a city due to x-diesel vehicles is given by P(x) = 0.005x3 + 0.02x2 + 30x. Find the marginal increase in pollution content when 3 diesel vehicles are added.
Answer» We have to find [P(x)]x = 3 Now, P(x) = 0.005x³ +0.002x² + 30x ∴ P(x) = 0.015x² + 0.04x + 30 ⇒ [P(x)]x = 3 = 0.015 x 9 + 0.04 x 3 + 30 = 0.135 + 0.12 + 30 = 30.255

The amount of pollution content added in air in a city due to x-diesel vehicles is given by P(x) = 0.005x3 + 0.02x2 + 30x. Find the marginal increase in pollution content when 3 diesel vehicles are added.

Answer»

We have to find

[P(x)]x = 3

Now,

P(x) = 0.005x³ +0.002x² + 30x

∴ P(x) = 0.015x² + 0.04x + 30

⇒ [P(x)]x = 3

= 0.015 x 9 + 0.04 x 3 + 30

= 0.135 + 0.12 + 30

= 30.255