What Are Critical Points?
Read this topicExplanations 2
- Here's some graphical intuition: The top of a hill is always flat. Good, "flat" at that point implies that the slope of the curve is 0 at that point. The first derivative test t…
By Ray Li, Victor Wang, Geoff Gaugler, Moor Xu, Alex Federspiel
- (Videos) Finding Critical Numbers by PatrickJMT Here's a video by patrickJMT where he shows you how to find critical points. A critical point is any point, that, when plugged in…
By Alex Federspiel
Problems 10
- Which of the following are critical points of f(x)=x4−2x2+2f(x) = x^4 - 2x^2 + 2f(x)=x4−2x2+2?
- What are the critical points for the function f(x)=6x22x2−4f(x)=\frac{6x^2}{2x^2-4}f(x)=2x2−46x2
- What are the critical points for the function f(x)=ln(cosx)f(x)=\ln(\cos x)f(x)=ln(cosx) on the interval π2<x<3π2\frac{\pi}2<x<\frac{3\pi}22π<x<23π
- What are the critical points for the function f(x)=e2x+5f(x)=e^{2x+5}f(x)=e2x+5
- What are the critical points for the function f(x)=3x3−4x+19f(x)=3x^3-4x+19f(x)=3x3−4x+19
- Select the functions that have an infinite amount of critical points.
- Select all the functions that only have x=0x=0x=0 as their critical point.
- What are the critical points for the function f(x)=5x2+8x+11f(x)=5x^2+8x+11f(x)=5x2+8x+11
- What is the sum of the critical values of the function f(x)=12x4+4x3−4x2−48x+ef(x)=\frac12x^4+4x^3-4x^2-48x+ef(x)=21x4+4x3−4x2−48x+e
- What is the sum of the critical values of the function f(x)=13x3−214x2+852x−394f(x)=\frac13x^3-214x^2+852x-394f(x)=31x3−214x2+852x−394