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Questions › DSE › DSE 2009 › Q28
2 marksMathematics › Limits, continuity and differentiability › Differentiability and its link to continuityModerateabout 3 min

DSE 2009 Question 28: Limits, continuity and differentiability

A function fff is defined by f(x)=x2f(x)=x^{2}f(x)=x2 if x≤cx\le cx≤c and f(x)=ax+bf(x)=ax+bf(x)=ax+b if x>cx>cx>c, where a,b,ca,b,ca,b,c are constants. Find values of aaa and bbb such that f′(c)f'(c)f′(c) exists.

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A function f is defined by f(x)=x² if x≤ c and f(x)=ax+b if x>c, where a,b,c are constants. Find values of a and b such that f′(c) exists. (A) a=2c, b=-c² (B) a=c, b=-2c² (C) a=3/2c, b=-1/c (D) a=1, b=ln c

Also written as: A function f is defined by f(x)=x^2 if x<= c and f(x)=ax+b if x>c, where a,b,c are constants. Find values of a and b such that f'(c) exists.

Limits, continuity and differentiability has come up 122 times in 7 exams since 2006.

What this question tests

This question is on Differentiability and its link to continuity, part of Limits, continuity and differentiability in Mathematics.

When a derivative exists and why differentiability implies continuity but not conversely.

TestStop has 12 past-paper questions on this subtopic; the nearest in year are below.

  • IIT JAM 2021 · Q35Let f be defined on (-π/2, π/2) by f(x) = (cos (π/2 + |x|))/(sin (π/2 - |x|)). Then,
  • IIT JAM 2022 · Q34Let f be defined by f(x) = |x| + |cos (π/2 - x)| for x ∈ (-π/2, π/2). Then
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Question from the DSE 2009 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.