IVP: A function f has the intermediate value property on an interval [a,b] if for all x<y in [a,b] and all L between f(x) and f(y), it is always possible to find a point c in (x,y) where f(c)=L And IVT: If f:[a,b]->R is continuous, and if L is a real number satisfying f(a)<L<f(b) or f(a)>L>f(b) then there exists a point c in (a,b) where f(c)=L Both definitions seem very similar to me, what purpose do they serve individually?

What is the derivative of the work function?

How to use implicit differentiation to find ${\displaystyle \frac{dy}{dx}}$ given ${\displaystyle 3x^2+3y^2=2}$?

How to differentiate $y=\log <!--\; \; -->x^2$?

The solution of a differential equation y′′+3y′+2y=0 is of the form
A) $c_1{e}^x+c_2{e}^{2x}$
B) $c_1{e}^{-<!--\; -\; -->x}+c_2{e}^{3x}$
C) $c_1{e}^{-<!--\; -\; -->x}+c_2{e}^{-<!--\; -\; -->2x}$
D) $c_1{e}^{-<!--\; -\; -->2x}+c_2{2}^{-<!--\; -\; -->x}$

How to find instantaneous velocity from a position vs. time graph?

How to implicitly differentiate ${\displaystyle \sqrt{xy}=x-2y}$?

What is 2xy differentiated implicitly?

How to find the sum of the infinite geometric series given ${\displaystyle 1+\frac{2}{3}+\frac{4}{9}+...}$?

Look at this series: 1.5, 2.3, 3.1, 3.9, ... What number should come next?
A. 4.2
B. 4.4
C. 4.7
D. 5.1

What is the derivative of ${\displaystyle \frac{x+1}{y}}$?

How to find the sum of the infinite geometric series 0.9 + 0.09 + 0.009 +…?

How to find the volume of a cone using an integral?

What is the surface area of the solid created by revolving ${\displaystyle f\left(x\right)=e^{2-x},x\in [1,2]}$ around the x axis?

How to differentiate ${\displaystyle x^{\frac{2}{3}}+y^{\frac{2}{3}}=4}$?

The differential coefficient of $\sec \left({\tan }^{-1}\left(x\right)\right)$.