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Find the difference quotient of the given function

label Algebra
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f(x)=2x^2 4x-3

Oct 8th, 2014

f(x) = 2x^2 + 4x - 3

Now first we find 

f(x + h) = 2(x + h)^2 + 4(x + h) - 3

             = 2(x^2 + h^2 + 2xh) + 4x + 4h - 3

             = 2x^2 + 2h^2 + 4xh + 4x + 4h - 3

We now substitute f(x + h) and f(x) in the definition of the difference quotient by their expressions

[ f (x + h) – f(x) ] / h    , then

= [2x^2 + 2h^2 + 4xh + 4x + 4h - 3 - (2x^2 + 4x - 3) ] / h

= [2x^2 + 2h^2 + 4xh + 4x + 4h - 3 - 2x^2 - 4x + 3) ] / h

= [ 2h^2 + 4xh + 4h ] / h

= h[ 2h + 4x + 4 ] / h

=  2h + 4x + 4 

= 2(h + 2x + 2)

= 2[h + 2(x + )]

Hence the difference quotient is   2[h + 2(x + )]

Oct 8th, 2014

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