Let f: R arrow R be given by f(x)=|x2-1|, x ∈ R. then

Question

Let f: R arrow R be given by f(x)=|x2-1|, x ∈ R. then (A) f has a local minimum at x=± 1 but no local maximum (B) f has a local maximum at x=0 but no local minimum (C) f has a local minima at x=± 1 and a local maxima at x=0 (D) f has neither a local maxima nor a local minima at any point

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/579d5ebceaead639a27bf39305142a27-.png" /> f has a local minima at x=± 1 and local maximum at x=0

Q. Let $f : R \to R$ be given by $f (x) = ∣ ∣ x^{2} - 1 ∣ ∣, x \in R$ . then

$f$ has a local minimum at $x = \pm 1$ but no local maximum

$f$ has a local maximum at $x = 0$ but no local minimum

$f$ has a local minima at $x = \pm 1$ and a local maxima at $x = 0$

$f$ has neither a local maxima nor a local minima at any point

$f$ has a local minima at $x = \pm 1$ and local maximum at $x = 0$

Q. Let f:R→R be given by f(x)=∣∣​x2−1∣∣​,x∈R. then

f has a local minimum at x=±1 but no local maximum

f has a local maximum at x=0 but no local minimum

f has a local minima at x=±1 and a local maxima at x=0

f has neither a local maxima nor a local minima at any point