Thread: Newbie to Derivative needs help

1. Newbie to Derivative needs help

There are 2 problems I am having particular trouble with.

QUESTION 1

A coal-burning electrical generating plant emits sulfur dioxide into the surrounding air. The concentration, C(x), in parts per million, is given approximately by C(x)= 0.1/x^2 where x is the distance from the plant in miles.

So the derivative is -.2x^-3 i believe?

And then I have to evaluate C(2) and C'(2).

C(2) = -.2(2)^3 = -.025

C'(2) = I am unsure of how to acquire this.

QUESTION 2

Use the definition of the derivative to find f'(x) if f(x) = x^3.

I know the derivative is 3x^2 but when I try to do it step by step by hand I get screwed up somewhere.

Any help or tips in the right direction would be appreciated.

2. Originally Posted by Zabulius
There are 2 problems I am having particular trouble with.

QUESTION 1

A coal-burning electrical generating plant emits sulfur dioxide into the surrounding air. The concentration, C(x), in parts per million, is given approximately by C(x)= 0.1/x^2 where x is the distance from the plant in miles.

So the derivative is -.2x^-3 i believe?

correct ... $\displaystyle C'(x) = -\frac{0.2}{x^3}$

And then I have to evaluate C(2) and C'(2).

C(2) = -.2(2)^3 = -.025

no ... $\displaystyle C(2) = \frac{0.1}{2^2}$

C'(2) = I am unsure of how to acquire this.

$\displaystyle C'(2) = -\frac{0.2}{2^3}$

QUESTION 2

Use the definition of the derivative to find f'(x) if f(x) = x^3.

below ...
$\displaystyle f(x+h) = (x+h)^3 = x^3 + 3x^2h + 3xh^2 + h^3$

$\displaystyle f(x) = x^3$

$\displaystyle f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$

$\displaystyle f'(x) = \lim_{h \to 0} \frac{(x^3 + 3x^2h + 3xh^2 + h^3) - (x^3)}{h}$

$\displaystyle f'(x) = \lim_{h \to 0} \frac{3x^2h + 3xh^2 + h^3}{h}$

$\displaystyle f'(x) = \lim_{h \to 0} \frac{h(3x^2 + 3xh + h^2)}{h}$

$\displaystyle f'(x) = \lim_{h \to 0} (3x^2 + 3xh + h^2) = 3x^2$

3. Much appreciated skeeter!