Intermediate Value Theorem (IVT)
Read this topicExplanations 3
- Here's another statement that seems so obvious it hardly needs justification: any continuous function, moving from one value to another, must pass through every real value betwe…
By Alexander Mason, Yiyi Rao, Moor Xu
- Continuous Function and IVT Statement This is a basic theorem in calculus. To know what it means, we first need to know what a continuous function is. We will assume you know wh…
By amaterasu, David Li, Victor Wang, Alex Federspiel
- (Video) Intermediate Value Theorem by PatrickJMT Here's a video by patrickJMT explaing the Intermediate Value Theorem. The Intermediate Value Theorem states: suppose you have a …
By Alex Federspiel, Expii Solve
Problems 11
- Does x3−2x2−3x+5=0x^3 - 2x^2 - 3x + 5 = 0x3−2x2−3x+5=0 have a solution in the interval (1,2)(1,2)(1,2)?
- Consider the equation 2x=x22^x = x^22x=x2. What does the Intermediate Value Theorem tell us about whether it has a solution in the interval (0,1)(0,1)(0,1)?
- Let fff be continuous, and suppose that the equation f(x)=0f(x) = 0f(x)=0 has no solution. True or false: f(x)>0f(x) > 0f(x)>0 for all xxx if and only if f(274)>0f(274) > 0f(274…
- Let fff be a continuous function such that f′f'f′ is also continuous. Suppose f(a)=2f(a) = 2f(a)=2 and f(b)=4f(b) = 4f(b)=4 for a<ba < ba<b. Also suppose that f′(a)=3f'(a) = 3f′…
- Does x4−x3+3x2−4x−3=0x^4-x^3+3x^2-4x-3=0x4−x3+3x2−4x−3=0 have a root in the interval [1,2][1,2][1,2]?
- Does 12x5+12x3−3x2+1=0\frac{1}{2}x^5+\frac{1}{2}x^3-3x^2+1=021x5+21x3−3x2+1=0 have a root in the interval [1,2][1,2][1,2]?
- Does 2x4−4x3+2x2+5x−2=02x^4-4x^3+2x^2+5x-2=02x4−4x3+2x2+5x−2=0 have a root in the interval [0,1][0,1][0,1]?
- Now suppose AAA and BBB start walking from rest with accelerations a1a_1a1 and a2a_2a2 (with a1<a2a_1 < a_2a1<a2), holding all other conditions the same. Then the equation w…
- Does sinx=x2\sin x=x^2sinx=x2 have a root in the interval [0,1][0,1][0,1]?
- Does tanx=3x\tan x=3xtanx=3x have a root in the interval [0.5,1][0.5,1][0.5,1]?
- There could have been a thick plot, or a lone actor. If it was a lone actor, who was it?