# Practical Differentiation help

• Jun 28th 2011, 01:34 AM
webb84
Practical Differentiation help
Hi

I have a practical differentiation question I just cant seem to solve,

Resistance to motion, F, of a moving vehicle is given by F = 5/X +100X, Determine the minimum value of resistance?

I think its the two x that are confusing me, the examples did in class all involved area and volume and were easy to grasp. any help would be appreciated.

regards
• Jun 28th 2011, 02:06 AM
Also sprach Zarathustra
Re: Practical Differentiation help
Quote:

Originally Posted by webb84
Hi

I have a practical differentiation question I just cant seem to solve,

Resistance to motion, F, of a moving vehicle is given by F = 5/X +100X, Determine the minimum value of resistance?

I think its the two x that are confusing me, the examples did in class all involved area and volume and were easy to grasp. any help would be appreciated.

regards

Solution with Inequality of arithmetic and geometric means - Wikipedia, the free encyclopedia

$\displaystyle F= \frac{5}{x} +100x \geq 2\sqrt{\frac{5}{x}100x}=2\sqrt{5\cdot100}=20\sqrt{ 5}$

Hence, the min of $\displaystyle F$ is $\displaystyle 20\sqrt{5}$.
• Jun 28th 2011, 03:55 AM
mr fantastic
Re: Practical Differentiation help
Quote:

Originally Posted by webb84
Hi

I have a practical differentiation question I just cant seem to solve,

Resistance to motion, F, of a moving vehicle is given by F = 5/X +100X, Determine the minimum value of resistance?

I think its the two x that are confusing me, the examples did in class all involved area and volume and were easy to grasp. any help would be appreciated.

regards

Start by solving dF/dx = 0. Have you tried doing this? Where do you get stuck?