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

The equation of motion of a stone,thrown vertically upwards is $s = ut - 6.3t^2$,where the units of $s$ and $t$ are $cm$ and $sec$. If the stone reaches its maximum height in $3$ $sec$,then $u =$ ......... $cm/sec$.

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

What is the maximum area of a rectangle that can be formed with a fixed perimeter $p \ cm$?

An open-topped box is to be constructed by removing equal squares from each corner of a $3 \text{ m}$ by $8 \text{ m}$ rectangular sheet of aluminium and folding up the sides. Find the volume of the largest such box.

For the function $f(x)=x^3-6x^2-12x-3$,$x=2$ is a

Vedclass Test Series

Exam Paper Generator

Online Exam Module