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May 25th, 2012, 03:31 PM   #1
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Tangent line equation


I'm having trouble with a quotient rule problem that asks you to find the equation of the tangent line.

The function is

The question then states that when x=9 the corresponding y value will be______ and the slope of the tangent line
Is f'(x)=9=_______.

Thererore the equation of the tangent line is_______? In form ax+b.

For the first blank I just inserted x=9 into the original equation and solved f(x)=-53.
For the second blank I got the slope equalling -55/9 by plugging x=9 into the derivative of f(x).

I Calculated the Derivative using the product rule

And ended up with a derivative of:

For the tangent line equation I got

By plugging in the coordinates (9,-53) to y+53=(-55/9)x-9

Some part here is incorrect I am not sure which, any help would be much appreciated
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May 25th, 2012, 03:39 PM   #2
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Re: Tangent line equation

If you plug x=9 into the derivative , you should get

. Also, , as you correctly have.

So, you now have x=9, y=-53, m=-163/18. All set to find line equation.

It may be a little easier to find the derivative by expanding f(x) into

Then, term-by-term, we get .

Or you can write it as I have above. Just another equivalent form.

Is that a picture of you with a TI?.

Good to see you're into math. Count yourself as a member of a small minority of the overall population.
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May 25th, 2012, 03:59 PM   #3
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Re: Tangent line equation

Though galactus mentioned it (while I was posting ), here is another approach:

Now it is a little easier to differentiate.

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May 25th, 2012, 10:32 PM   #4
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Re: Tangent line equation

Ya thanks guys I haven't dealt with product quotient rules in awhile so the different approaches are very helpful as i get back into things. And ya galactus I've always enjoyed math, although the program I'm in is calling for less and less of it as I near the end, unfortunately..
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