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Limits and Derivatives — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSLimits and Derivatives1 Mark
MCQ
Is Rolle’s theorem valid for f(x) = x2 - 3x + 4 in the interval [1, 2]?
  • A
    Yes
  • B
    No
  • C
    Depends on x
  • D
    Data not sufficient
✓

Answer

  1. Yes

Solution:

Obviously, f(x) is continuous at [1, 2]

And, f(x) differentiable at [1, 2]

Also, f(1) = f(2) = 2

Now, f(x) = 0

⇒ 2x - 3 = 0

$⇒ \text{x} = \frac{3}{2}$

Thus, x belongs to [1, 2]

Hence, it is verified.

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