Using `LMVT,` prove that if two functions have equal derivatives at all points of `(a, b)`,then they differ by a constant

Prove that the greatest integer function [x] is continuous at all points except at integer points.

Find the derivative of the following function at the indicated point: x"\ "a t"\ "x=1

Prove that two triangles having the same base and equal areas lie between the same parallels.

Find the derivative of the function at the indicated point: sin x \ at \ x=pi/2

Which of the following statements are true and which are false; All squares are congruent. If two squares have equal areas, they are congruent. If two rectangles have equal areas, they are congruent. If two triangles have equal areas, they are congruent.

The first and second order derivatives of a function f(x) exit at all point in (a,b) with f'( c) =0 , where altcltb , of c and f'(x)gt0 for all points on the immediate right of c, and f'(x)lt0 for all points on the immediate left of c then at x=c , , f(x) has a

Prove that the line of centres of two intersecting circles subtends equal angles at the two points of intersection

If f and g are two functions having derivative of order three for all x satisfying f(x)g(x)=C (constant) and (f''')/(f')-"A" (f'')/f -(g''')/(g')+(3g")/g=0 . Then A is equal to

If it is know that at the point x = 1 two anti- derivatives of f(x) = e^(x) differ by 2, the difference of the anti - derivatives at x = 100 is :

In the curve x^a y^b=K^(a+b) , prove that the potion of the tangent intercepted between the coordinate axes is divided at its points of contact into segments which are in a constant ratio. (All the constants being positive).