A new chapter!
We are finally done with chapter 3, a very interesting chapter that included so much information.
Now we are on to chapter 4; the zeros of the derivative is the local minimum and maximums of the original function! We just learned section 4.1 yesterday, and this was a spoiler that my table group discovered, or maybe we learned this before but we now came in the realization of it.
We are finally done with chapter 3, a very interesting chapter that included so much information.
Now we are on to chapter 4; the zeros of the derivative is the local minimum and maximums of the original function! We just learned section 4.1 yesterday, and this was a spoiler that my table group discovered, or maybe we learned this before but we now came in the realization of it.
Local Extrema:
A local max/min is a function value (f(a)) that is the highest or lowest in a given "area". Yet all absolute extrema are also local extrema.
So for the example below, the local max is at x=-1 and the local min is x=1 for the interval [-1.5,1.5].
A local max/min is a function value (f(a)) that is the highest or lowest in a given "area". Yet all absolute extrema are also local extrema.
So for the example below, the local max is at x=-1 and the local min is x=1 for the interval [-1.5,1.5].
For this next example, we find the derivative and plug in the x in order to find the f(x) to figure out if it is a max or min. So we plugged in x=6,8,1 to find the values -10,14, and 35. These values show if they are concave up or concave down.
To find "y"...
you plug in the "x" into f(x) of the original function to find the min/max value.
you plug in the "x" into f(x) of the original function to find the min/max value.
Here are my additional notes for finding the critical points and finding the absolute extremas!