Post #12

This week in Calculus we reviewed, took tests, and learned linearization. I don’t really know how to work a problem like that, but im not sure we did one in class..so it’s cool. My question has got to be that I don’t know how to look at a graph and find out every little aspect of it. Can someone PLEASE tell me how to figure out graphs..every part of them.
So, this week I’ll explain the topics I keep getting wrong because I forget how to do it..i know the steps I just blank out during the test, so hopefully typing them out on here will help me remember.

TANGENT LINE:
1. Take derivative of your equation.2. Plug x in to DERIVATIVE to find your slope, M3. Plug in x to ORIGINAL to find y-intercepts4. Now, use m and (x,y) plug it into the equation (y-y1)=m(x-x1).

Example Problem:

Y = 2x^2+7x at x = 1
= 4x + 7 Plug in x to find slope
= 4(1) +7 = 11 m = 11
2(1)^2+7(1) = 9 y = 9
= y-9 = 11(x-1)

HORIZONTAL TANGENTS:

This is super easy, I just always forget what to do when they give you an equation and say find the horizontal tangent.
So, first, you take the derivative; set it equal to zero, solve for x.

Example Problem:

y = x^3 + 12x^2 + 5 3x^2 + 24x = 0 3x ( x + 8) = 0Horizontal Tangents at X = 0, x = -8
Please, if anyone can help me with the free response graph problems..they are probably put on the test as giveaways, but I don’t understand how to figure out the horizontal tangents of f’ when they give you f’’, or f. Help please?