Given that C(x)=2x^3-21x^2+36x+1000 is a cost function, determine the intervals for which the cost is increasing. Determine any intervals for which the marginal cost is increasing.
Marginal cost is when you derive the cost function, correct? So do you do the second derivative for the marginal cost intervals?
(So far, I just did the first derivative and got negative infinity to 1 and 6 to infinity to be my answers, but are those right or wrong, and would they count for marginal cost or regular cost?)
You are correct, both in your calculations and your understanding of the concepts.
C is increasing when C' > 0
C' = 6x^2-42x+36
= 6(x^2-7x+6)
= 6(x-1)(x-6)
C'>0 for x<1 or x>6
The marginal cost is C', so C' is increasing when C">0.
C" = 6(2x-7)
C">0 when x > 7/2