## X=5

#### Topics

Applications of the Derivative

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##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

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### Video Transcript

Okay. So for this problem, they give us an equation of 10,000 times one minus 0.95 to the X power most one over X. And they just want to know what X gives us the minimum value. So to minimise this s o the average equals that this is our objective equation. And we only have one variable, so we don't really need constraints here. So we take the derivative. It'll have the same zero if we drop this 10,000 or not. Eso The derivative is just negative. Natural log of 0.95 at times 0.95 to the X and that minus one over x squared. Okay, In lieu of trying to solve this algebraic lee, I just grafted to see where it crosses the X axis. Um, so just be careful in your in your calculators. Um, make sure you put parentheses around that natural auger pregnancies around the 0.95 just to make sure it doesn't evaluate Natural. Got the whole thing. Sometimes calculators can give a hiccup with natural log. Um, it crosses the X axis somewhere close to fot 5.2 And since the closest group size to 5.2 is five. Then get with the group size of five to have the minimum number of tests, and that's all, thank you very much.

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Kennesaw State University

#### Topics

Applications of the Derivative

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

Lectures

Join Bootcamp