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I have a math extremum problem, but I am unable to solve it.

"Car gasoline use per hour is: $w = 6 - 0.15v + 0.0025v^2$. At what speed does the car have to travel, so that it would be cheapest. "

I used derivative to find a global minimum and got $30$km/h, but my textbook says the correct answer is $49$km/h.

Can anyone help?

Thank you in advance!

Maazul
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user63021
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1 Answers1

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Your are right

$$w=6+\frac{v^2-60v}{400}=6+\frac{(v-30)^2-900}{400}\ge 6-\frac94$$, the minimum value occurs if $v=30$

lab bhattacharjee
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