Simplify the difference quotient f2 h f2 if h notequalto 0

Simplify the difference quotient f(2 + h) - f(2) if h notequalto 0. f(x) = x^2 - 7x h - 30 Simplify the difference quotient f(x + h) - f(x)/h if h notequalto 0. f(x) = x^2 + 31 h + 2xh + 62 Simplify the difference quotient f(x + h) - f(x)/h if h notequalto 0. f(x) = 39/x^2

Solution

3)

given f(x)=x²-7x

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

difference coefficient =[((2+h)²-7(2+h))-(2²-7*2)]_/h

difference coefficient =[(4+4h+h²-14-7h)-(4-14)]_/h

difference coefficient =[4h+h²-7h]_/h

difference coefficient =4+h-7

difference coefficient =h-3

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4)

given f(x)=x²+31

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

difference coefficient =[((x+h)²+31)-(x²+31)]_/h

difference coefficient =[(x²+2xh+h²+31)-(x²+31)]_/h

difference coefficient =[2xh+h²]_/h

difference coefficient =2x+ h

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5)

given f(x)=(39/x²)

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

difference coefficient =[(39/(x+h)²)-(39/x²)]_/h

difference coefficient =39[(1/(x+h)²)-(1/x²)]_/h

difference coefficient =39(x²-(x+h)²)_{/[hx²(x+h)²]}

difference coefficient =39(-2xh+h²)_{/[hx²(x+h)²]}

difference coefficient =39(-2x+h)_{/[x²(x+h)²]}