Let f be differentiable on [a,b] and suppose that k is a number between f'(a) and f'(b). Then there exists a point c ε (a,b) such that f'(c)=k.
GREEN'S THEOREM: if m=m(x,y) and n= n(x,y) are the continuous functions and also partial differential in a region 'r' of x,y plane bounded by a simple closed curve c. DIVERGENCE THEOREM: if f is a vector point function having continuous first order partial derivatives in the region v bounded by a closed curve s
A cubic has from 1 to 3 real solutions. The fact that every cubic equation with real coefficients has at least 1 real solution comes from the intermediate value theorem. The discriminant of the equation tells you how many roots there are.
derivatives are the functions required to find the turning point of curve
They are derivatives with respect to measures in space: normally length, area or volume.
Yes.
Yes. Derivatives are instruments of investment for the knowledgeable financial people. Novice and intermediate investors should keep away from derivatives.
The acronym "IVT" stands for something. It stands for Intermediate Value Theorem. This is a mathematical formula that can be used to solve an equation.
The intermediate axis theorem is important in the study of rotational motion and stability because it explains the behavior of an object rotating around its intermediate axis. This theorem helps predict how objects will rotate and maintain stability, especially in situations where the rotation is not around the principal axes. Understanding this theorem is crucial for analyzing the motion and stability of rotating objects in various scenarios.
the Pythagorean theorem helps find the value of the longest side in a right triangle if you know the value of the base and the height.
It is multiplied by 2 if the intermediate reaction is multiplied by 2
I suggest: - Take the derivative of the function - Find its initial value, which could be done with the initial value theorem That value is the slope of the original function.
If a function is continuous on [a, b], differentiable on (a, b), and it is zero at a and b (f(a) = 0 and f(b) = 0), then there must be some value c such that a < c < b where the derivative is zero (means the tangent line above or below c will be a horizontal tangent).
Basic calculus is about the study of functions. The two main divisions of calculus are differentiation and integration. Differentiation has to do with finding the tangent line to a function at any given point on the function. Integration has to do with finding the area under (or above) a curve. Other topics covered in calculus include: Differential equations Approximations of functions (linear approximation, series, Taylor series) Function analysis (Intermediate Value Theorem, Mean Value Theorem)
GREEN'S THEOREM: if m=m(x,y) and n= n(x,y) are the continuous functions and also partial differential in a region 'r' of x,y plane bounded by a simple closed curve c. DIVERGENCE THEOREM: if f is a vector point function having continuous first order partial derivatives in the region v bounded by a closed curve s
A cubic has from 1 to 3 real solutions. The fact that every cubic equation with real coefficients has at least 1 real solution comes from the intermediate value theorem. The discriminant of the equation tells you how many roots there are.
Lagrang Theorem was discvered in 2008 by Yogesh Shukla
The Pythagorean Theorem allows the mathematician to determine the value of the hypotenuse. The converse of the Pythagorean Theorem manipulates the formula so that the mathematician can use the values to determine that if the triangle is a right triangle.