Derivatives at Local Extrema
Read this topicExplanations 3
- Fermat's Theorem states that all relative extrema of a function lie at critical numbers. Be careful, though; the converse of Fermat's Theorem does not hold. A critical number of…
By Sujay Kazi
- (Video) Finding Intervals of Increase, Decrease, Local Maximums, and Local Minimums by PatrickJMT Here's a video by patrickJMT where he shows you how to apply the first derivati…
By Alex Federspiel
- (Video) Second Derivative Test to Find Local Extrema by PatrickJMT Here's a video by patrickJMT where he shows you how to use the second derivative test in order to figure out i…
By Alex Federspiel
Problems 13
- Let aaa be a real number and consider the function f(x)=x4−x3−x2+ax+1f(x) = x^4 - x^3 - x^2 + ax + 1f(x)=x4−x3−x2+ax+1. Suppose fff has a local minimum at aaa, and f(a)=af(a) = …
- Using the cost of gasoline function, find an interval on which the function appears to be decreasing. Estimate any local extrema using the table.
- Use the derivative test to find the local maximum points of the function f(x)=2x2x2+4f(x)=\frac{2x^2}{x^2+4}f(x)=x2+42x2
- Use the derivative test to find the local minimum points of the function f(x)=2x2x2+4f(x)=\frac{2x^2}{x^2+4}f(x)=x2+42x2
- Use the derivative test to find the local maximum points of the function f(x)=14x4+x3−92x2−27x+9f(x)=\frac14x^4+x^3-\frac92x^2-27x+9f(x)=41x4+x3−29x2−27x+9
- Use the derivative test to find the local minimum points of the function f(x)=14x4+x3−92x2−27x+9f(x)=\frac14x^4+x^3-\frac92x^2-27x+9f(x)=41x4+x3−29x2−27x+9
- Use the derivative test to find the local minimum points of the function f(x)=(x2−4)2f(x)=(x^2-4)^2f(x)=(x2−4)2
- Use the derivative test to find the local maximum points of the function f(x)=(x2−4)2f(x)=(x^2-4)^2f(x)=(x2−4)2
- Use the derivative test to find the local minimum points of the function f(x)=2x3+1f(x)=2x^3+1f(x)=2x3+1
- Use the derivative test to find the local maximum points of the function f(x)=2x3+1f(x)=2x^3+1f(x)=2x3+1
- You're reading "Surely You're Joking, Mr. Feynman!", but there's a word smeared out: I often liked to play tricks on people when I was at MIT. One time, in mechanical drawing cl…
- We define Gabriel's Modified Horn as the shape generated when we revolve y=1xαy = \frac{1}{x^{\alpha}}y=xα1 around the xxx-axis for x≥1,x \geq 1,x≥1, where α>12\alpha > \frac{1…
- We define Gabriel's Modified Horn as the shape generated when we revolve y=1xαy = \frac{1}{x^{\alpha}}y=xα1 around the xxx-axis for x≥1,x \geq 1,x≥1, where α>12\alpha > \frac{1…