So there goes the seventh week of calculus.
This past week after taking the quiz on optimization we were given our study guides for the exam. By the way I still need some help on optimization so if anyone has gotten the hang of that please let me know if you are willing to teach me. I'm finally getting the hang of everything, especially derivatives and tangent lines.
I'll do an example of a tangent line for you:
Write the equation of the tangent line to the graph of g at x=3. g(x)=x^2 - 4x + 9
First of all, you are given an x value. To find the y value, you simply just plug in the x into the original equation.
g(3)=(3)^2 -4(3) + 9
g(3) = 6
This gives you the point (3,6) which you will use later to write the equation.
Now you have to find the slope. This just means to take the derivative and then plug in the given x.
g'(x)=2x-4
g'(3)=2(3) - 4
g'(3)=2
Now that you have a point and a slope, guess what you do now..
Put it in point slope form :)
y-y1=m(x - x1)
so you're tangent line would be y-6=2(x-3)
Another problem I have is limits (aka chapter 1). If anyone is able to help guide me with that packet it'd be greatly appreciated. I know all the rules so don't comment me the rules, i just can't put them into play..
Oh and also remember that when it asks you at what value is the slope of the graph equal to a number, all you do is take the derivative and set it equal to that number then solve for x.
Anyways, I still have a lot of work to do and always accepting help.
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For limits, if you are trying to find the lim as it approaches 2- you have to cover up the right side and see where the graph is approaching. If it was just 2 you would have to cover up both sides to see where they are approaching and if they match that is the limit, if not it does not exist. If you are trying to find something like f(1) you plug into the equation that fits 1 and that is your limit. I hope this helps.
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