21?

okay so i think everyone will agree that the first week back to calculus was extremely roughhhh. I suck at practice AP's but hopefully i'll get better at them.

i'm just going to review some things that we all may need to know.

Equation of a tangent line:
Take the derivative and plug in the x value.
If you are not given a y value, plug into the original equation to get the y value.
then plug those numbers into point slope form: y − y1 = m(x − x1)

Finding critical values:
To find critical values, first take the derivative of the function and set it equal to zero, solve for x. The answers you get for x are your critical values.

Absolute extrema:
If you are given a point, plug those numbers into the original function to get another number. Alos, solve for critical values and plug those into the original function. Once you get your second numbers, you set each pair into new sets of points. The highest point is the absolute max and the smallest point is the absolute min.

LRAM- left hand approximation.
x[f(a)+f(a+x)+...f(b)]
RRAM- right hand approximation.
x[f(a+x)+...f(b)]
MRAM- approximation from the middle.
x[f(mid)+f(mid)+...]

Trapezoidal- this does not use squares, instead it uses trapezoids to eliminate most of the empty space inside the curve, and I think this is the most accurate. x/2[f(a)+2f(a+x)+2f(a+2x)+...f(b)]

Example: Find the area of f(x)x-3 on the interval [0,2] with 4 subintervals.
delta x=2-0/4=1/2

LRAM=1/2[f(0)+f(1/2)+f(1)+f(3/2)]
1/2[-3+-5/2+-2+-3/2]
1/2[-9]= -9/2

RRAM=1/2[f(1/2)+f(1)+(3/2)+f(2)]
1/2[-5/2+-2+-3/2+-1]
1/2[-7]= -7/2

MRAM=1/2[f(1/4)+f(3/4)+f(5/4)+f(7/4)]
1/2[-11/4+-9/4+-7/4+-5/4]
1/2[-8]= 4

Trapezoidal=1/4[f(0)+2f(1/2)+2f(1)+2f(7/2)+f(2)]
1/4[-3+-10/2+-4+-6/2+-1]
1/4[-16]= 4


as far as questions go.. i have trouble understanding what exactly it is i'm being asked to do on the AP test. umm other things.. substitution, it'd be great if anyone would like to review that for me.