Consider the function f(x) = |x - 2| + |x - 5 | vedclass

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

Question

(C) For $x \in [2, 5]$,the function is defined as $f(x) = (x - 2) - (x - 5) = 3$.Since $f(x) = 3$ is a constant function on the interval $[2, 5]$,its

Vedclass · Accepted Answer

Statement-$1$ is true,Statement-$2$ is true; Statement-$2$ is the correct explanation for Statement-$1$.

Vedclass · Answer

(C) For $x \in [2, 5]$,the function is defined as $f(x) = (x - 2) - (x - 5) = 3$.Since $f(x) = 3$ is a constant function on the interval $[2, 5]$,its derivative $f'(x) = 0$ for all $x \in (2, 5)$.Thus,$f'(4) = 0$,so Statement-$1$ is true.For Statement-$2$,$f(x) = |x - 2| + |x - 5|$ is a sum of continuous functions,hence continuous on $[2, 5]$.On the interval $(2, 5)$,$f(x) = 3$,which is a constant function and therefore differentiable.Also,$f(2) = |2 - 2| + |2 - 5| = 3$ and $f(5) = |5 - 2| + |5 - 5| = 3$,so $f(2) = f(5)$.Statement-$2$ is true.Since $f(x)$ is constant on $[2, 5]$,its derivative is zero everywhere in $(2, 5)$,which directly explains why $f'(4) = 0$. Thus,Statement-$2$ is the correct explanation for Statement-$1$.

Consider the function $f(x) = |x - 2| + |x - 5|, x \in R$.
Statement-$1$: $f'(4) = 0$.
Statement-$2$: $f$ is continuous in $[2, 5]$,differentiable in $(2, 5)$ and $f(2) = f(5)$.

Similar Questions

If $f(x) = (x - 1)(x - 2)(x - 3)$ for $x \in [0, 4]$,then the value of $c \in (0, 4)$ satisfying Lagrange's mean value theorem is

Let $f: [-1, 2] \rightarrow R$ be a differentiable function such that $0 \le f'(t) \le 1$ for $t \in [-1, 0]$ and $-1 \le f'(t) \le 0$ for $t \in [0, 2]$. Then:

If from the Mean Value Theorem,$f'({x_1}) = \frac{f(b) - f(a)}{b - a}$,then

Let $f(x)$ be a function continuous on $[1, 2]$ and differentiable on $(1, 2)$ satisfying $f(1) = 2, f(2) = 3$ and $f'(x) \geq 1$ for all $x \in (1, 2)$. Define $g(x) = \int_1^x f(t) \, dt$ for all $x \in [1, 2]$. Then the greatest value of $g(x)$ on $[1, 2]$ is-

Let $f$ be continuous on $[1, 5]$ and differentiable in $(1, 5).$ If $f(1)=-3$ and $f'(x) \ge 9$ for all $x \in (1, 5)$,then which of the following is true?

Vedclass Test Series

Exam Paper Generator

Online Exam Module

Consider the function $f(x) = |x - 2| + |x - 5|, x \in R$.Statement-$1$: $f'(4) = 0$.Statement-$2$: $f$ is continuous in $[2, 5]$,differentiable in $(2, 5)$ and $f(2) = f(5)$.