Lyndon Essay Samples and Topic Ideas

Lyndon 82) f'x=x-2ddx x2-2x+4-/(x-2)2first derivative=x2-4x(x-2)2 Where if fx=0, the critical points are 0 and 4Function increases for x<0 , x>4 Decreases for 0<x<4f). the local maxima and the local minima from the first derivative x=0 or 4When x=0, f0=-2, f-1=-73, f1=-3 , hence x=0 is the local maximaWhen x=4, f3=7 , f4=6, f-5=193hence x=4 is the local minima g) The intervals for concave up and down we get the second derivative using the quotient rule f''x=8(x-2)3When second derivative=0 , x=2 by choosing two auxiliary points x=0 and x=3 it follows that f''0=-1 hence -∞,2 the curve is concave downward ) And f''3=8 hence 2, ∞ the curve is concave upward...