Summary of Optimization on Closed Intervals
Read this topicExplanations 2
- Optimization is determining minima and maxima of a function. This is one of the many useful practical applications of calculus. Given a function fff on a closed interval [a,b][a…
By Alexandr Wang, Ahaan Rungta, Alex Federspiel
- (Video) The Closed Interval Method by PatrickJMT Here's a video by patrickJMT explaining the Closed Interval Method and how to use it to find absolute maximums and minimums. He …
By Alex Federspiel
Problems 10
- What is the maximum value of y=x−x3y = x - x^3y=x−x3 in the range of 0<x<10 < x < 10<x<1?
- Find the maximum value of f(x)=x+1xf(x) = x + \frac1xf(x)=x+x1 on the interval [0.2,4][0.2,4][0.2,4].
- Find the minimum value of f(x)=x+1xf(x) = x+\frac1xf(x)=x+x1 on the interval [0.2,4][0.2,4][0.2,4].
- Find the maximum value of f(x)=cos(2x)+2sinxf(x) = \cos(2x) + 2\sin xf(x)=cos(2x)+2sinx on the interval [0,π2][0, \frac\pi2][0,2π].
- What is the absolute minimum of f(x)=3x3−4x2+24f(x)=3x^3-4x^2+24f(x)=3x3−4x2+24 on the interval [−3,5][-3,5][−3,5]?
- What is the absolute maximum of f(x)=3x3−4x2+24f(x)=3x^3-4x^2+24f(x)=3x3−4x2+24 on the interval [−3,5][-3,5][−3,5]?
- What is the absolute minimum of f(x)=ln(x2−1)f(x)=\ln(x^2-1)f(x)=ln(x2−1) on the interval [−2,2][-2,2][−2,2]?
- What is the absolute maximum of f(x)=ln(x2−1)f(x)=\ln(x^2-1)f(x)=ln(x2−1) on the interval [−2,2][-2,2][−2,2]?
- What is the absolute minimum of f(x)=1−x3+x2+x−2f(x)=\dfrac{1}{-x^3+x^2+x-2}f(x)=−x3+x2+x−21 on the interval [−1,32][-1,\frac32][−1,23]?
- What is the absolute maximum of f(x)=1−x3+x2+x−2f(x)=\dfrac{1}{-x^3+x^2+x-2}f(x)=−x3+x2+x−21 on the interval [−1,32][-1,\frac32][−1,23]?