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..

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). ..

Use Rolle's Theorem to determine the value of c such that f ′ ( c ) = 0, if f ( x ) = x 2 - 1 in the interval [- 1, 1]. => - 2 or 0 or 2 or - 1 or 1..

Use Rolle's Theorem to determine the value of c such that f ′ ( c ) = 0, if f ( x ) = x x + 5 in the interval [- 5, 0]. => 0 or 10 3 or - 10 3 or - 13 or - 5..

Use Rolle's Theorem to determine the value of c such that f ′ ( c ) = 0, if f ( x ) = 1 - x 2 in the interval [- 1, 1]. => 1 or - 1 or 0 or - 2 or 1 2..

Use Rolle's Theorem to determine the value of c such that f ′ ( c ) = 0, if f ( x ) = x ( x + 3) e - x 2 in the interval [- 3, 0]. => 0 or - 3 or - 2.5 or - 2 or - 1..

Use Rolle's Theorem to determine the value of c such that f ′( c ) = 0, if f ( x ) = log ( x 2 + 1 2 - 2 x ) in the interval [- 4, - 3]. => - 2 2 or - 4 3 or 1 4 or - 1 4 or - 2 3..

Use Rolle's Theorem to determine the value of c such that f ′( c ) = 0, if f ( x ) = sin 2 x in the interval [0, 3 π 2 ]. => π 2 , 3 π 2 or 3 π 2 or π, 2π or π 4 , 3 π 4 or 0..

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,..