GATE EE 2017 Set 1 — Question 26
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Engineering Mathematics → Calculus
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Question
A function is defined as , where . Which one of the following statements is TRUE?
Correct answer
(B) f(x) is differentiable at x = 1 for the unique values of a and b.
Solution
For to be differentiable at , it must first be continuous at .
Continuity at :Differentiability at :For differentiability, the left-hand derivative must equal the right-hand derivative:Subtracting equation (1) from (2):Substituting into (1):Since there is a unique pair of values for which the function is differentiable, option (B) is correct.
Continuity at :Differentiability at :For differentiability, the left-hand derivative must equal the right-hand derivative:Subtracting equation (1) from (2):Substituting into (1):Since there is a unique pair of values for which the function is differentiable, option (B) is correct.
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