Question 1181030


Critical points are points where the function is defined and its derivative is zero or undefined.

{{{y=x^(7/2) - 7x^2}}}, {{{x>0}}}

derivate:

{{{y}}}'{{{(x) = (7/2)x* (x^(3/2) - 4)}}}

{{{(7/2)x* (x^(3/2) - 4)=0}}}

=>{{{(7/2)x=0}}}=>{{{x=0}}}=> exclude because given {{{x>0}}}

=>{{{x^(3/2) - 4=0}}}=>{{{x^(3/2) = 4}}}=>{{{sqrt(x^3) = 4}}}
=>{{{x^3 = 16}}}=>{{{x = 2* 2^(1/3)}}}


Critical point is at  {{{x = 2* 2^(1/3)}}}.