First slide

Mean value theorems

Question

$Let f be a continuous function in [0, 3] and differentiable in (0, 3) such that f (3) = 0 .$ $Then there exist some α \in (0, 3) such that$

Difficult

A

$α f^{1} (α) - f (α) = 0$
B

$2 α f^{1} (α) - 3 f (α) = 0$
C

$3 α f^{1} (α) - f (α) = 0$
D

$α f^{1} (α) + f (α) = 0$

Solution

$\begin{array}{l} Let g (x) = x^{n} f (x) (n > 0) \\ g (0) = 0, g (3) = 0 \\ By using rolls theorem, there exist some α \in (0, 3) such that \end{array}$
$g^{1} (α) = 0 \Rightarrow α f^{1} (α) + n f (α) = 0, n > 0$
$W e c a n s e e t h a t f o r n = 1, o p t i o n (4) i s t r u e .$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App