## Answers

The volume as a function of x is given by:

V(x)=x(x+5)(10-x)=-x^3+5*x^2+50*x

To find the maximum volume, we differentiate V(x) with respect to x and equate the derivative to zero:

dV/dx = -3*x^2+10*x+50 =0

Solve for x to get:

x=-2.7 or x=6.08

We reject the negative value of x to retain

x=6.08.

To check if the Volume is a maximum, we calculate

V"(6.08)=d²V/dx²=10-6x=-26.48<0

so V(6.08) is a maximum..

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