Let be the statement '' and be the statement 'the function has no stationary point'. Which of the following is correct? (Here is a real number.)
Answer and explanation
Correct answer: C. is both a necessary and a sufficient condition for
- Step 1: . There is a stationary point exactly when has a real solution, i.e. when .
- Step 2: So there is no stationary point exactly when : the statements are equivalent.
Answer
is both a necessary and a sufficient condition for .
Why not the others: For the derivative vanishes at , so fails both statements; no value of separates them.
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