MathsCBSE Class 12 · Board exam 2024, set 65/5/1 · 2 marks · Very short answer

CBSE Class 12 Mathematics 2024: question 22(b)

Set in the CBSE Class 12 board exam of 2024, paper 65/5/1, section B, question 22(b), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q22(b) · 2 marks · Very short answerContinuity and Differentiability

Check for differentiability of the function f defined by $f (x) = ∣ x - 5∣$ , at the point $x = 5$ .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 65/5/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

Write $∣ x - 5∣$ without modulus separately for $x < 5$ and $x > 5$ .

Hint 2

Find the left-hand and right-hand derivatives using $\frac{f ( x ) - f ( 5 )}{x - 5}$ and compare them.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

$f (5) = 0$ . LHD $= lim_{x \to 5^{-}} \frac{∣ x - 5∣ - 0}{x - 5} = lim_{x \to 5^{-}} \frac{- ( x - 5 )}{x - 5} = - 1$ .
1 mark
RHD $= lim_{x \to 5^{+}} \frac{∣ x - 5∣ - 0}{x - 5} = lim_{x \to 5^{+}} \frac{x - 5}{x - 5} = 1$ .
½ mark
Since LHD $\neq =$ RHD, f is not differentiable at $x = 5$ .
½ mark

Answer: LHD = −1, RHD = 1; f is not differentiable at x = 5.

Where the marks are

Computes LHD $= - 1$ (1 mark)
Computes RHD $= 1$ (½ mark)
Concludes not differentiable since LHD ≠ RHD (½ mark)

Revise the chapter

Chapter: Continuity and Differentiability (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Continuity and Differentiability, one at a time, marked against the answer key and marking points.Back to the full paper2024 board paper, set 65/5/1: every question, by section.

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CBSE Class 12 Mathematics 2024: question 22(b)

Hints

Step-by-step solution

Revise the chapter

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