Calculus: Absolute Maximum Minimum for Polynomial First Derivative Application

Absolute Maximum and Absolute minimum value for any function continuous in closed interval [a, b] will always exist at the critical numbers or at the end points.
Check the value of the function at the critical numbers and at the end-points to find the result.
Steps to find increasing and decreasing interval of any function, f(x), are:
find the first derivative, f'(x)
find critical numbers, f'(x) = 0 or does not exist (DNE)
INTERVAL TABLE TEST:
These critical numbers divide the domain in intervals. Test each interval with a test point.
RESULT:
If f'(x) is greater than 0 then f(x) is increasing.
If f'(x) is less than 0 then f(x) is decreasing.
#calculus #derivativeapplication #increasinginterval #decreasinginterval #mcv4u #anilkumar #globalmathinstitute #absolutemaximum #absoluteminimum

[amanjha]

Love you sir mathapachhi best way that everybody understand

[mohammadjaved]

Sir how to determine maxima minima of linear equation.
Viz. If x+y+z=9 then find maximum value of 2x^2+y^2+z^2

[abdelelfazari]

Thanks big man this helped me solve a question i was stumped on

[firasshakoor]

what about x^4 + x^2 + 5? whats the min point?

[genoyostevon]

why don't you go a step further and find critical numbers or point of inflection by doing the second derivative .... it wouldn't be that much more work