CBSE Class 12 Mathematics sample paper 2023-24: question 17
From the official CBSE sample question paper for 2023-24, section A, question 17, for 1 mark. Try it first; the hints and our step-by-step solution are below.
Q17 · 1 mark · MCQContinuity and Differentiability
The set of all points where the function is differentiable, is
- (A)
- (B)
- (C)
- (D)
Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2023-24.
Hints
Open one hint at a time and try again before the next.
Hint 1
Write piecewise.
Hint 2
Compare the left and right derivatives at 0.
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.
for and for . At , and , so is not differentiable there.
- 1 mark
On each side of 0 the function is linear or constant, so it is differentiable everywhere else: , option (C).
Answer: , option (C)
Where the marks are
- Shows and differentiability elsewhere (1 mark)
Revise the chapter
- Chapter: Continuity and Differentiability (notes, formulas, where marks are lost and every past question)
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