TS EAMCET · Maths · Continuity and Differentiability
A function \(y=f(x)\) with \(f(-1)=-249\) has no maximum and has only one minimum at \(x=5\) with \(f(5)=75\). Which one of the following is true?
- A At some point in \((-1,5), f(x)\) is discontinuous
- B The minimum value cannot be 75 since \(f(-1) < f(5)=75\)
- C \(f(x)\) is discontinuous at every point of \(\mathbf{R}\)
- D \(f(x)\) is continuous on \(\mathbf{R}\)
Answer & Solution
Correct Answer
(A) At some point in \((-1,5), f(x)\) is discontinuous
Step-by-step Solution
Detailed explanation
It is given that there is a function \(y=f(x)\) such that it have no maximum but has only one minimum at \(x=5\) with \(f(5)=75\), but \(f(-1)=-249\) is given, so it is only possible the function is not continuous in \((-1,5)\).
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