Reflection

This week we reviewed from a previous chapter, these are the steps to rolle’s theorem, finding extrema, max or mins.

Rolle Theorem:
1. Make sure it is continuous.
2. Make sure it is differentiable.
3. Make sure the y-values match.
4. Take the derivative, set = 0, and solve for x.
example of the Rolle Theorem.
EXAMPLE:
Let f(x) = x^4 - 2x^2
Find all values c in the interval (-2, 2) such that f'(c) = 0.
1. ok
2. ok
3. f(-2) = (-2)^4 - 2(-2) = 8
f(2) = (2)^4 -2(2)^2 = 8
4. f'(x) = 4x^3 - 4x = 0
4x(x^2 - 1) = 0
x = 0, + or – 1

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.

First Derivative Test:
1. take derivative and set it equal to zero.
2. find anywhere it is not differentiable
3. set up intervals using steps 1 and 2.
4. plug in a number on the interval into the derivative equation
5. if +ve it is increasing. if it is -ve it is decreasing
6. determine max or mins.
increasing- max
decreasing- min