SOLUTION: If {{{p(x)=2sqrt(x-5)+3x}}}, what is the minimum value of P?

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Question 1043530: If p%28x%29=2sqrt%28x-5%29%2B3x, what is the minimum value of P?
Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.
If p%28x%29 = 2sqrt%28x-5%29%2B3x, what is the minimum value of P?
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The square root part domain is x >= 5.
So, it is the domain for the entire p(x).

In this domain sqrt%28x-5%29 monotonically grows.
3x monotonically grows too.

Hence, p(x) monotonically grows.
It implies that the minimum value of p(x) is at x = 5. You can easily calculate it.



Figure. Plot f(x) = 2sqrt%28x-5%29%2B3x