Find (x+h) for f(x)=3x^2

1 answer:

6 0

F(x) = 3x2+5x-2, find [f(x+h)-f(x)]/h

f(x+h) = 3(x+h)2 + 5(x+h) - 2
= 3(x2 + 2xh + h2)+ 5x + 5h -2
= 3x2 + 6xh + 3h2 + 5x + 5h - 2

f(x+h)-f(x) = 3x2 + 6xh + 3h2 + 5x + 5h - 2 - (3x2+5x-2)

= 6xh + 3h2 + 5h

[f(x+h)-f(x)]/h = (6xh + 3h2 + 5h)/h

= h(6x + 3h + 5)/h

= 6x + 3h + 5

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