Question #91814

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Question #91814

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Answer 1 · 2016-11-03T22:00:25

Write the expression. Expand. Simplify.

Explanation:

$f(x) = 5x^2+3x$

Remember that $x$ is the name of whatever is inside the parentheses"

$f("this") = 5("this")^2+3("this")$

So, $f(x+h) = 5(x+h)^2+3(x+h)$

You also need to know (be able to find) $(x+h)^2 = x^2+2xh+h^2$ .

Here we go:

$(f(x+h)-f(x))/h = ([5(x+h)^2+3(x+h)] - [5x^2+3x])/h$

$= ([5(x^2+2xh+h^2)+3(x+h)] - [5x^2+3x])/h$

$= (5x^2+10xh+5h^2+3x+3h - 5x^2 - 3x)/h$

$= (10xh+5h^2+3h)/h$

$= (h(10x+5h+3))/h$

$= (10x+5h+3)$ $" "$ for $h != 0$ .

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Question #91814

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