Continuity and Differentiability — Class 12 Maths Solution

exemplar objective MCQ NCERT Exemp. Ex.5.3 ,Q.95,Page 115
Question

The value of $c$ in Rolle's theorem for the function $f(x) = {x^3} - 3x$ in the interval $[0,\sqrt 3 ]$ is

  • (a) 1 ✓ Correct
  • (b) -1
  • (c) $\frac{3}{2}$
  • (d) $\frac{1}{3}$
Step-by-step Solution
Correct answer: option (a)

$\Rightarrow$ $\quad 3{c^2} - 3 = 0$

$\Rightarrow$ ${c^2} = \frac{3}{3} = 1$

$\Rightarrow$ $c = \pm 1,$ where $1 \in (0,\sqrt 3 )$
therefore,$\quad c = 1$

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NCERT & Exemplar solution for CBSE Class 12 Mathematics, Continuity and Differentiability. Curated by Sachin Sharma. Free for all students.