Let f ( x ) = 1 − x 3 for x ≤ 1 , and f ( x ) = x − 1 + λ for x > 1 . Which statement is true?

Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeMaxima-MinimaMedium2 minQB

MathematicsMediumsingle choice

Let $f (x) = 1 - x^{3}$ for $x \leq 1$ , and $f (x) = x - 1 + λ$ for $x > 1$ . Which statement is true?

Options:

Answer:

Solution:

$f (1) = 0$ , and values just to the left are positive. For every $λ > 0$ , values immediately to the right are also positive, so $x = 1$ is a strict local minimum. (In fact $λ = 0$ also gives a local minimum; option D is a true sufficient statement, not an iff claim.)

Stream:JEESubject:MathematicsTopic:Application of DerivativeSubtopic:Maxima-Minima

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