POST 36

Q:An equation of the line tangent to the graph of y=cos(2x) at x=pi/4 is
tangent line steps: take derivative, plug in x to get slope, use point slope formula, and if not given y plug x value into original

A: cos(2x)
-2sin(2x)
-2sin2(pi/4)
-2sin(pi/2)
-2=slope

cos(2(pi/4))
cos(pi/2)=0

y=-2(x-pi/4)


3. Let f be a function defined for all real numbers x. If f^1(x)=(4-x^2)/x2, then f is decreasing on the interval *(4-x^2 is really the absolute value of 4-x^2)

first derivative test!
f^1(x)=(4-x^2)/x2 =0
4-x^2=0
-x$2=4
x=+ or - 2

(-infinity,-2) (-2,2) (2,infinity)
plug in -3=-ve/decreasing
plug in 0=-ve/decreasing
plug in 3=+ve/increasing

So decreasing on the interval (-infinity,2)

The limit rules are:
1. if the degree of the top is bigger than the degree of the bottom, the limit is infinity.
2. if the degree of the top is smaller than the degree of the bottom, the limit is 0.
3. if the degree of the top is equal to the degree of the bottom, the limit is the coefficient of the leading term of the top divided by the coefficient of the leading term of the bottom equation.


The steps for optimization are:
1. Identify all quantities
2. Write an equation
3. Reduce equation
4. Determine domain of equation
5. Determine max/min values

The steps to find maximums and minimums are:
1. First derivative test
2. Plug critical values into the original function to get y-values
3. Plug endpoints into the original function to get y-values
4. The highest y-value is the absolute maximum
5. The lowest y-value is the absolute minimum


The steps for related rates are:
1.Pick out all variables
2. Pick out all equations
3. Pick out what you are looking for
4. Sketch a graph and label
5. Create an equation with your variables
6. Take the derivative respecting time
7. Substitute back into the derivative
8. Solve

DONT KNOW LIMITS!!!!!!!!!!!!!!!!