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 + )]
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