Blog 14

Thanksgiving holidays are almost over :( they flew by so fast! Hopefully everyone had a good holiday! Since we didn’t have school this week I’ll just explain 3.5 which is horizontal asymptotes, and I’ll also explain the short cut to the first derivative test. Horizontal asymptote: To find a horizontal asymptote you take the limit as x is approaching infinity. Y=# is the horizontal asymptote. To take the limit you just simply use the limit rules. If the degree of the top is equal to the degree of the bottom the answer is the coefficients. Example: x^2+2/x^2-1=1, If the degree of the top is greater than the degree of the bottom then the horizontal asymptote is either negative infinity or infinity. Example: x^2+2/x-1=infinity, If the degree of the bottom is greater than the degree of the top then the horizontal asymptote is zero. Example: x^2+2/x^3-1=0.

Now the short cut to the first derivative test:

There are four steps:
1. First derivative, set equal to zero, solve.
2. Is it differentiable?
3. Take second derivative; Plug critical points into second derivative.
4. If positive number then it’s a MIN, if negative number then it’s a MAX (May seem odd, but it’s the rule so memorize it) and If 0 then the test fails.

Example:
Find the relative extrema for f(x)=-3x^5+5x^3
1. -15x^4+15x^2=0
15x^2(-x^2+1)
X=0,+/- 1

2. All polynomials are differentiable!
3. -60x^2+30x
4. -60(0)^3+30(0)=0;FAILS
-60(-1)^3+30(-1)=Positive number;MIN
-60(1)^3+30(1)=Negative number;MAX

I pretty much understand everything; I just need more practice on it all. Minus the graphs, I don’t get that at all.