Answer to Question #90630 in Calculus for JEET GURUNG

Question

Determine maximum value of y if y=100/x+4x

Answer 1

To find extrema we need to take the derivative of function y(x) and equate it to zero. This leads to equation 100/x²-4=0 with the roots x=5 and x=-5. The first root x=5 corresponds to relative minimum because the second derivative at this point is positive: y''(x)=200/x³>0 for x>0, and the second one corresponds to a relative maximum because y''(-5)=-8/5<0.

Answer: y(x) has the relative maximum y=-40 at the point x=-5.