Find the difference quotient fx h fxh y x2 2x Solution1

Find the difference quotient f(x + h) - f(x)/h ? y = x^2 - 2x

Solution

1) f(x)=y =x² -2x

f(x+h)=(x+h)²-2(x+h)

f(x+h)=x²+2xh +h²-2x-2h

f(x+h)-f(x)=x²+2xh +h²-2x-2h -x² +2x

f(x+h)-f(x)=2xh +h²-2h

difference coefficient =[f(x+h)-f(x)]/h

difference coefficient =[2xh +h²-2h ]/h

difference coefficient =2x +h-2

2) f(x)=(2/x)

f(x+h)=(2/(x+h))

f(x+h)-f(x)=(2/x) -(2/(x+h))

difference coefficient =[f(x+h)-f(x)]/h

difference coefficient =[(2/x) -(2/(x+h))]/h

difference coefficient =2 [(1/x) -(1/(x+h))]/h

difference coefficient =2 [(1/x) -(1/(x+h))]/h

difference coefficient =2 [(x+h) -x]/(hx(x+h))

multiply and divide by ((x+h) +x)

difference coefficient =2 [((x+h) -x)((x+h) +x)]/(hx(x+h)((x+h) +x))

difference coefficient =2 [x+h -x]/(hx(x+h)((x+h) +x))

difference coefficient =2 [h ]/(hx(x+h)((x+h) +x))

difference coefficient =2 /(x(x+h)((x+h) +x))