I need help optimizing this function. Lots of big numbers that confuse me.

Question

937 * (2520x)^0.75 + 749 (2520-2520x)^0.75 - 106760

Optimize this function. I know you have to take the derivative and then set that equal to zero and solve for x but I dont understand how to do this with such big numbers and a complex set up... please help.

Answer 1

you're right! so there are three parts:

derivative of 937(2520x)^0.75 is (0.75*937)(2520x)^{0.75 - 1}(2520), or 1770930(2520x)^-0.25

derivative of 749 (2520-2520x)^0.75 is (0.75*749)(2520-2520x)^{0.75 - 1}(-2520), or -1415610(2520-2520x)^-0.25

derivative of -106760 is 0, because it's a constant.

so your derivative is 1770930(2520x)^-0.25 - 1415610(2520-2520x)^-0.25. Set equal to zero, and now it gets easier.

you should get x close to 0.71.