Compute the derivative of g(t) if g(t)=√t^3+3t+1?
Also, Compute the derivative of g(t) if g(t)=√t^3+3t+1. C(q)=p+hq+(k/q)where p,h, and k are constants. Suppose p=4 , h=1 , and k=8 . What is the economic order quantity? In other words, find the value of q that minimizes the cost C(q) with q>0 .
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Don't ever write a radical sign without an inclusion sign (parentheses or brackets).
How do we know if you mean sqrt(t^3+3t+1) or sqrt(t^3+3t) + 1, or something else?
Anyway, the derivative of sqrt(t^3+3t+1) is
(3t^2+3)/ [2 sqrt(t^3+3t+1)].
If C(q) = 4 + q + 8/q, then C'(q) = 1 - 8/q^2.
C'(q) will be 0 when 1=8/q^2, i.e., q = sqrt(8) = about 2.828.
This is a minimum (rather than a maximum) because C"(2.828) = +16/(8 sqrt(8)) > 0.