i have already completed the question im just using this as an example

For question c i found f'(x) then i found the value of x via simple algebra manipulation

but what if the question asks for the maxmimum value of P??

YEEEEEET Jan 8, 2019

#1**+1 **

If you have the value of 'x' that minimizes P...... Sub that value in to the equation for P to find the minumum value of P.

ElectricPavlov Jan 8, 2019

#3**+1 **

Your question asks for the MINIMUM value of P........ There likely is no MAXIMUM value of P....you can make the perimetr as large as you want.

ElectricPavlov
Jan 8, 2019

#4**+1 **

P = 100x^(-1) + x ( pi + 8 - 2sqrt(3)/ 4 take the derivative, set to 0

P' = -100x^(-2) + ( pi + 8 - 2sqrt (3) ) / 4 = 0 multiply through by x^2

[ ( pi + 8 - 2sqrt (3) / 4 ] x^2 - 100 = 0

[ pi + 8 - 2sqrt (3) ] x^2 = 400

x^2 = 400 / [ pi + 8 - 2sqrt (3) ] take the positive root

x = 7.218

Sub this back into P to find the minimum P ≈ 27. 7 m

We can verify that this is the minimum ........

P " = 200/ x^3

Subbing in x = 7.218 will produce a positive....thus...x = 7.218 produces a minimum value

CPhill Jan 8, 2019