Let f: R rightarrow R be given by f(x) = |x^{ | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The function is defined as $f(x) = |x^{2} - 1|$.We can analyze the behavior of the function by looking at its graph or by testing points.At $x = \

Vedclass · Accepted Answer

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

Vedclass · Answer

(C) The function is defined as $f(x) = |x^{2} - 1|$.We can analyze the behavior of the function by looking at its graph or by testing points.At $x = \pm 1$, $f(x) = |(\pm 1)^{2} - 1| = |1 - 1| = 0$. Since the absolute value function is always non-negative, $f(x) \geq 0$ for all $x \in R$. Thus, $f(x) = 0$ at $x = \pm 1$ represents the absolute minimum value of the function, which is also a local minimum.At $x = 0$, $f(0) = |0^{2} - 1| = |-1| = 1$. For values of $x$ close to $0$, say $x = 0.1$ or $x = -0.1$, $f(0.1) = |(0.1)^{2} - 1| = |0.01 - 1| = 0.99$. Since $f(0) = 1 > 0.99$, $x = 0$ is a point of local maximum.Therefore, $f$ has local minima at $x = \pm 1$ and a local maximum at $x = 0$.

Let $f: R \rightarrow R$ be given by $f(x) = |x^{2} - 1|$, $x \in R$. Then:

Similar Questions

If a ball is thrown vertically upwards and the height $s$ reached in time $t$ is given by $s = 22t - 11t^{2}$, then the total distance travelled by the ball is (in $\text{ units}$)

Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in $sq.m$) of the flowerbed is

The radius (in $cm$) of the right circular cylinder of greatest curved surface area which can be inscribed in a given cone with radius $10 \ cm$ is

The maximum value of $f(x) = \sin (x)$ in the interval $[-\pi / 2, \pi / 2]$ is

If $f(x) = x^5 - 5x^4 + 5x^3 - 10$ has local maximum and minimum at $x = p$ and $x = q$,respectively,then $(p, q)$ equals

Vedclass Test Series

Exam Paper Generator

Online Exam Module