Posted by Dan on Thursday, November 4, 2010 at 7:00am.
Find f'(x) and see if there is a zero (root) on the interval.
If not, the extrema are the two limits of the interval.
Check the sign of f'(x) on the interval. If there is no zero on the interval, the sign should not change (+ OR -).
If f'(x) is + on the interval, it is monotonically increasing, and vice versa.
If it is monotonically increasing or decreasing, then f(c1) and f(c1) are the limits of the range of the function on the given interval [c1,c2]. I.e. the function does not take up values beyond [f(c1),f(c2)].
Post your answer for checking if you wish.
Related Questions
Calculus - f(x)=xe^(-2x) with domain 0< or equal to x< or equal to...
Calculus (pleas help!!!) - Find the absolute maximum and absolute minimum ...
Calculus (pleas help!!!) - Find the absolute maximum and absolute minimum values...
Calculus - Find the value of the derivative at each indicated extremum.
Calculus - Determine where the absolute extrema of f(x)=-3(x^2)+7x on the ...
calculus - 2. Consider the function f defined by f(x)=(e^X)cosx with domain[0,...
calculus - 2. Consider the function f defined by f(x)=(e^X)cosx with domain[0,...
calculus - Find the absolute maximum and absolute minimum values of f on the ...
calculus - Find the absolute maximum and absolute minimum values of f on the ...
Calculus - another question - "Find the absolute minimum value of the ...
For Further Reading
