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Limits and Derivatives — Maths STD 11 Science — Question

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

Answer

Correct option: A.
Yes
Obviously, $f(x)$ is continuous at $[1, 2]$
And, $f(x)$ differentiable at $[1, 2]$
Also, $f(1) = f(2) = 2$
Now, $f(x) = 0$
$\Rightarrow 2x - 3 = 0$
$\Rightarrow \text{x} = \frac{3}{2}$
Thus, $x$ belongs to $[1, 2]$
Hence, it is verified.

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