Question

The marginal cost of a product is modeled by:
14/cube root of 14x+5. Where x is the number of units. X=15, C=120.
a) Find the cost function C=
b) Find the Cost in dollars of producing 80 units

I am lost as how to get the fraction at the beginnning of the next step, What is the trick, or rule that I can't seem to learn>!>!!!?????

Answer 1

Dc/dx=14/³√(14x+5)

C=14∫1/³√(14x+5)dx

Put u=14x+5
Du/dx=14

Dx=du/14

C=14∫(u^-1/3)du/14=14/14(u^(2/3)/(2/3))+c

C=3/2(³√(14x+5))²+c
120=3/2(³√(14(15)+5))²+c

2/3(120)=(³√((5.99))²+c

80=35.8+c

c=80-35.8=34.2

C=3/2(³√(14(80)+5))²+34.2=3/2(108.16)+34.2=162.24+34.2=196.44

Check the maths for possible typo