A wire of length 10cm is cut into 2 pieces. One of these pieces is bent to form an equilateral triangle of side xcm. The other piece is bent to form a sector of a circle of angle theta radians and radius xcm. a)show that 5x + xtheta= 10 b)the sum of the area of the triangle and the sector is denoted by Acm^2 i)show that A=root3/4x^2 - 5/2x +5x ii)differentiate to find the value of x for which A has a stationary value. iii)differentiate again to determine whether this stationary value is a maximum or a minimum.

Question

A wire of length 10cm is cut into 2 pieces. One of these pieces is bent to form an equilateral triangle of side xcm. The other piece is bent to form a sector of a circle of angle theta radians and radius xcm.  a)show that 5x + xtheta= 10 b)the sum of the area of the triangle and the sector is denoted by Acm^2 i)show that A=root3/4x^2 - 5/2x +5x ii)differentiate to find the value of x for which A has a stationary value. iii)differentiate again to determine whether this stationary value is a maximum or a minimum.