Let f:R to R be a function defined by f(x) = | vedclass

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

Question

(D) To find the points where $f(x) = \max(x, x^3)$ is not differentiable,we analyze the behavior of $x$ and $x^3$ in different intervals:$1$. If $x <

Vedclass · Accepted Answer

$\{ - 1, 0, 1\}$

Vedclass · Answer

(D) To find the points where $f(x) = \max(x, x^3)$ is not differentiable,we analyze the behavior of $x$ and $x^3$ in different intervals:$1$. If $x $2$. If $-1  x$,so $f(x) = x^3$.$3$. If $0  x^3$,so $f(x) = x$.$4$. If $x > 1$,then $x^3 > x$,so $f(x) = x^3$.At the transition points $x = -1, 0, 1$,we check the left-hand and right-hand derivatives:At $x = -1$: $f'( -1^-) = 1$ and $f'( -1^+) = 3(-1)^2 = 3$. Since $1 
eq 3$,it is not differentiable.At $x = 0$: $f'( 0^-) = 3(0)^2 = 0$ and $f'( 0^+) = 1$. Since $0 
eq 1$,it is not differentiable.At $x = 1$: $f'( 1^-) = 1$ and $f'( 1^+) = 3(1)^2 = 3$. Since $1 
eq 3$,it is not differentiable.Thus,the set of points where $f(x)$ is not differentiable is $\{ -1, 0, 1\}$.

Let $f:R \to R$ be a function defined by $f(x) = \max \,(x, x^3).$ The set of all points where $f(x)$ is not differentiable is

Similar Questions

If $y = \sec^{-1} \left( \frac{2x}{1 + x^2} \right) + \sin^{-1} \left( \frac{x - 1}{x + 1} \right)$,then $\frac{dy}{dx}$ is equal to

If $f(x) = \begin{cases} \frac{1}{2}(b^2 - a^2), & 0 \leq x \leq a \\ \frac{1}{2}b^2 - \frac{x^2}{6} - \frac{a^3}{3x}, & a < x \leq b \\ \frac{1}{3}\left(\frac{b^3 - a^3}{x}\right), & x > b \end{cases}$,then which of the following is true?

$f(x) = \cos^{-1}(2x^2 - 1)$ is not differentiable at $x = a$,then $a$ equals:

If $f(x)$ is a differentiable function such that $f: R \to R$ and $f\left( \frac{1}{n} \right) = 0$ for all $n \ge 1, n \in I$,then:

If $f(x) = \begin{cases} \frac{x-1}{2x^2-7x+5}, & \text{for } x \neq 1 \\ -\frac{1}{3}, & \text{for } x=1 \end{cases}$,then $f^{\prime}(1)$ is equal to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module