rolle's theorem in calculus

Let f be a real valued function in [a,b] such that f is continuous in [a,b]. f is differentiable in (a,b..

Rolle's Theorem: Let f be a real valued function in [a,b] such that f is continuous in [a,b]. f is differentiable in (a,b). ..

Check if f (a) = f (b) If all the above condition are satisfied, then Rolle's theorem is applicable else the Rolle's theorem is not applicable. If Rolle's theorem is applicable, solve f '(c) = 0. Show that one of these roots lie in the op..

Derivatives are also used to trace the graphs of different functions. To optimise the value of a differentiable function of practical use, derivatives of the functions are applied. This chapter reveals with many more application of derivatives such as determining the relative error in measurement,..

1. If m = 0 the tangent at (x 1 , y 1 ) is parallel to x-axis. 2. If m 1 = m 2 the curves touch each other. 3. Rolle's theorem 4. Langrange's Mean Value theorem 5. Maxima and Mini..

Conclusion - In this chapter we have learnt the application of derivatives to rate measure, also we have used the geometrical measurement of to find the equations of the tangent and normal to a curve at any point on the curve, angle of intersection of the curves. The derivatives also help in examin..

x = a is called a point of inflexion. Rolle's theorem: If a function f(x) is such that (i) f (x) is continuous on [a,b] (ii) f (x) is differentiable on (a,b) and (iii) f (a) = f (b) Geometrical interpretation of Rolle's theorem Let AB be the graph of y = f(x)..

If x is a rational number, then the sum (e x ) of the exponential series..

Let f be continuous on [a, b] and differentiable on the open interval (a, b). Then (a) f is increasing on [a, b] if f '(x) > 0 for each x (a, b) (b) f is decreasing on [a, b] if f '(x) < 0 for each x (a, b) This theorem can be proved by using Mean Value Theorem. We sh..

Let f be real valued function in [a,b] such that, f is continuous in [a,b]. f is differentiable in (a,b)...