Sign chart for extrema
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A sign chart for extrema shows us the x-values of extrema on our function, and how the slope behaves surrounding them.
An extrema is a peak or valley on a function.
The very fact that it's a peak means...
- That the peak's slope is zero.
- That surrounding the peak, the slope changes from positive to negative (or vice-versa).
Scenario: Create a sign chart for extrema of f(x) below.
Remember: we want to find the x-values for extrema... a.k.a. where the slope equals zero!
Now, we need to find whether f'(x) is positive or negative at each of those "?" values!
Plugging in any number less than -1...
...results in a positive slope value, which we can plug into our sign chart like so:
Plugging in any number between -1 and 1...
...results in a negative slope value, which we can plug in like so.
Plugging in any number greater than 1...
...results in a positive slope value, which we can plug into our sign chart like so:
