# Tricky difference quotient problem i am stuck

## Homework Statement

find f(a+h)-f(a)/h for the f (x)= 2x+3x2

f(a+h)-f(a)/h

## The Attempt at a Solution

f(a+h)-f(a)/h
=2(a+h)-3(a+h)2-2x+3x2
=2a+2h-3a2-3h2-2a+3a2
=2h-3h2/h

that is where i am stuck

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First, what is $$(a + h)^{2}$$ ?

And what is $$-f(a)$$ equivalent to?

whoops, (a+h)^2 = a^2+2ah+h^2
but -f(a) is correct right?

notice the second line you wrote ($$2(a+h)-3(a+h)^{2}-2x+3x^{2}$$)

See something wrong with the last term ?

Mark44
Mentor

## Homework Statement

find f(a+h)-f(a)/h for the f (x)= 2x+3x2

f(a+h)-f(a)/h

## The Attempt at a Solution

f(a+h)-f(a)/h
You need more parentheses here.
This should be (f(a + h) - f(a))/h
=2(a+h)-3(a+h)2-2x+3x2
What happened to the h divisor? And as above, the entire numerator needs parentheses around it.
=2a+2h-3a2-3h2-2a+3a2
Still missing the h.
=2h-3h2/h

that is where i am stuck

so 2a+2h-3a^2-6ah-6h^2-2a+3a^2
=2h-6ah-6h^2/h
=2h(3a+3)/h
then what

oh ok i see

No, this is still not correct - you are doing your algebra wrong

$$f(a + h) - f(a) =$$
$$f(a + h) - (2x + 3x^{2}) =$$
$$f(a + h) + (-1)*(2x + 3x^{2})$$

You are not distributing the minus sign correctly

can you see how to fix it?

yes, sorry my eyes are not working,
so i got it down to 2h+6ah+3h^2/h
so the answer has to be 6a+3h+2
if not don't bother i quit
No, this is still not correct - you are doing your algebra wrong

$$f(a + h) - f(a) =$$
$$f(a + h) - (2x + 3x^{2}) =$$
$$f(a + h) + (-1)*(2x + 3x^{2})$$

You are not distributing the minus sign correctly

can you see how to fix it?

Mentallic
Homework Helper
And the limit is h approaches 0 so you cancel out the h. You can always check your answer by just taking the derivative of the function.