SOLUTION: How do you find the local minimum, local maximum, absolute minimum, absolute maximum, and increasing and decreasing in a function?
Algebra ->
Rational-functions
-> SOLUTION: How do you find the local minimum, local maximum, absolute minimum, absolute maximum, and increasing and decreasing in a function?
Log On
Question 214447: How do you find the local minimum, local maximum, absolute minimum, absolute maximum, and increasing and decreasing in a function? Answer by solver91311(24713) (Show Source):
If the first derivative of a function is positive over an interval, then the function is increasing on that interval. If the first derivative is negative over that interval, the function is decreasing over that interval.
A critical point of a function is a point such that or does not exist.
An absolute maximum or minimum over an interval is either a critical point in that interval or an endpoint of .
If you have a continuous and twice differentiable function, take the first derivative, set it equal to zero, and then solve. The roots will be critical points that can be either local minima or local maxima. Now take the second derivative and evaluate it at the value of each root from the previous step. If the value of the 2nd derivative is positive, then the curve is concave up and you have a local minimum. If the 2nd derivative is negative, you have a local maximum.
