InterviewSolution
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InterviewSolution
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Let `a, b in RR` and `f : RR rarr RR` be defined by `f(x) = a cos(|x^3-x|) + b|x| sin(|x^3+x|).` Then `f` isA. differentiable at x=0, if a=0 and b=1B. differentiable at x=1, if a=1 and b=0C. not differentiable at x=0, if a=1 and b=0D. not differerntiable at x=1, if a=1 and b=1 |
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Answer» Correct Answer - A::B We have `f(x)=a cos(|x^(3)-x|)+b|x|sin(|x^(3)+x|)"for all"x in R` `Rightarrow f(x)=a cos(x^(3)-x)+bx sin(x^(3)+x)"for all "x in R` Clearly, f(x) is the sum of two continuous and differentiable functions for all `x in R`. Hence options (a) and (b) are correct. |
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