Question #91814

1 Answer
Jim H
Nov 3, 2016

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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