Holiday Reflection #3

Here are some formulas and theorems to remember for after the holidays. They mostly deal with taking derivatives.


Steps for finding extremas, maxs, or mins:

1. Take the derivative and set it equal to zero. Solve for x.
2. Find anywhere the function isn’t differentiable.
3. Plug in to get a y-value if the problem is asking about a max or min specifically.
4. Set up intervals.
5. The highest number is the max & the lowest number is the min.

*When asked to find critical numbers, you just do the first two steps.

Rolle's Theorem:

1. Make sure the function is continuous.
2. Make sure the function is differentiable.
3. Make sure the y values match.
4. Take the derivative and set it equal to zero, then solve for x.

Mean Value Theorem (MVT):

-Similar to Rolle’s Theorem but after you do the first to steps you have to set the derivative equal to the slope of the function and solve for x.