# Math Help - Practical Differentiation help

1. ## 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

2. ## Re: Practical Differentiation help

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

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

Hence, the min of $F$ is $20\sqrt{5}$.

3. ## Re: Practical Differentiation help

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?