The set of all points where the function f(x) | vedclass

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

Question

(A) The function is given by $f(x) = 2x|x|$.We can rewrite this as a piecewise function:$f(x) = \begin{cases} 2x^2, & x \geq 0 \ -2x^2, & x < 0 \end{

Vedclass · Accepted Answer

$(-\infty, \infty)$

Vedclass · Answer

(A) The function is given by $f(x) = 2x|x|$.We can rewrite this as a piecewise function:$f(x) = \begin{cases} 2x^2, & x \geq 0 \ -2x^2, & x Since $2x^2$ and $-2x^2$ are polynomials,$f(x)$ is differentiable for all $x 
eq 0$. We only need to check the differentiability at $x = 0$.Left Hand Derivative $(LHD)$ at $x = 0$:$f'(0^-) = \lim_{h ightarrow 0^-} \frac{f(0+h) - f(0)}{h} = \lim_{h ightarrow 0^-} \frac{-2h^2 - 0}{h} = \lim_{h ightarrow 0^-} (-2h) = 0$.Right Hand Derivative $(RHD)$ at $x = 0$:$f'(0^+) = \lim_{h ightarrow 0^+} \frac{f(0+h) - f(0)}{h} = \lim_{h ightarrow 0^+} \frac{2h^2 - 0}{h} = \lim_{h ightarrow 0^+} (2h) = 0$.Since $LHD = RHD = 0$,the function $f(x)$ is differentiable at $x = 0$.Therefore,$f(x)$ is differentiable for all $x \in (-\infty, \infty)$.

The set of all points where the function $f(x) = 2x|x|$ is differentiable is

Similar Questions

Let $S = \{(\lambda, \mu) \in R \times R : f(t) = (\|\lambda\|e^{\|t\|} - \mu) \sin(2\|t\|), t \in R\}$ be a differentiable function. Then $S$ is a subset of?

Let $f(x) = \begin{cases} a \cot^{-1} \left( \frac{b+x}{4} \right), & \frac{-2}{3} < x < 0 \\ 2, & x = 0 \\ \frac{\ln(1-cx)}{x}, & 0 < x < \frac{2}{3} \end{cases}$. If the function $f(x)$ is differentiable at $x = 0$,then find the value of $(b^2 - 2a + c^6)$.

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?

If $f(x) = \begin{cases} x + 2, & -1 < x < 3 \\ 5, & x = 3 \\ 8 - x, & x > 3 \end{cases}$,then at $x = 3$,$f'(x) = $

$f(x)= \begin{cases} 2a-x & \text{in } -a < x < a \\ 3x-2a & \text{in } a \leq x \end{cases}$
Then,which of the following is true?

Vedclass Test Series

Exam Paper Generator

Online Exam Module