CBSE (Science) Class 12CBSE
Share
Notifications

View all notifications
Books Shortlist
Your shortlist is empty

Solution for C = 3 2 ∈ ( 1 , 2 ) the Value of C in Rolle'S Theorem for the Function F (X) = X3 − 3x in the Interval [0, √ 3 ] is (A) 1 (B) −1 (C) 3/2 (D) 1/3 - CBSE (Science) Class 12 - Mathematics

Login
Create free account


      Forgot password?

Question

\[c = \frac{3}{2} \in \left( 1, 2 \right)\]The value of c in Rolle's theorem for the function f (x) = x3 − 3x in the interval [0,\[\sqrt{3}\]] is 

(a) 1
(b) −1
(c) 3/2
(d) 1/3

Solution

(a) 1
The given function is \[f\left( x \right) = x^3 - 3x\] .

This is a polynomial function, which is continuous and derivable in R.
Therefore, the function is continuous on [0,\[\sqrt{3}\]] and derivable on (0,\[\sqrt{3}\])

Differentiating the given function with respect to x, we get 

\[f'\left( x \right) = 3 x^2 - 3\]

\[ \Rightarrow f'\left( c \right) = 3 c^2 - 3\]

\[ \therefore f'\left( c \right) = 0 \]

\[ \Rightarrow 3 c^2 - 3 = 0\]

\[ \Rightarrow c^2 = 1\]

\[ \Rightarrow c = \pm 1\]

Thus,

\[c = 1 \in \left[ 0, \sqrt{3} \right]\] for which Rolle's theorem holds.

Hence, the required value of c is 1.

  Is there an error in this question or solution?
Solution for question: C = 3 2 ∈ ( 1 , 2 ) the Value of C in Rolle'S Theorem for the Function F (X) = X3 − 3x in the Interval [0, √ 3 ] is (A) 1 (B) −1 (C) 3/2 (D) 1/3 concept: Maximum and Minimum Values of a Function in a Closed Interval. For the courses CBSE (Science), PUC Karnataka Science, CBSE (Arts), CBSE (Commerce)
S
View in app×