12th Math Practical No. 10 ~ Application of Derivatives 2

12th Mathematics practical book answers pdf Maharashtra board 

 ~Application of Derivatives 2

1) Rolle's Theorem

Rolle's theorem states that if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b) such that f(a) = f(b), then f′(x) = 0 for some x with a ≤ x ≤ b.

2) What Is Lagrange Mean Value Theorem?

The Lagrange mean value theorem states that if a function f is continuous over the closed interval [a,b], and differentiable over the open interval (a,b), then there exists at least one point c in the interval (a,b) such that the slope of the tangent at the point c is equal to the slope of the secant through the endpoints of the curve such that f'(c) = f(b)−f(a)/b−a

3) What is maxima and minima of a function?

Maxima and minima of a function are the largest and smallest value of the function respectively either within a given range or on the entire domain. Collectively they are also known as extrema of the function. The maxima and minima are the respective plurals of maximum and minimum of a function.

4) Steps to find maxima and minimum

    1.find derivative of x

    2.Set value of f'(x)=0, thus we will get value of x

    3.Take second derivative

    4.Put value of x from step 2 in second derivative

    5.If x=a and f''(x) > 0 then its Minima

    6.If x=b and f''(x)<0 then its Maxima

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