Question

Let \( f(x)=x|x| \). (a) Skatch the graph of the function. (1) Oroace B Oroace D Contce C Cumace (1) (b) For what values of \( x \) is \( f \) differentiable? \[ \begin{array}{l} 0 x \geq 0 \\ x<0 \\ x>0 \\ x \neq 0 \\ \text { all real } x \end{array} \] (c) Find a formula for \( f^{\prime} \) ', \[ f^{\prime}(x)=\square x \]

          Let \( f(x)=x|x| \).
(a) Skatch the graph of the function.
(1)
Oroace B
Oroace D
Contce C
Cumace
(1)
(b) For what values of \( x \) is \( f \) differentiable?
\[
\begin{array}{l}
0 x \geq 0 \\
x<0 \\
x>0 \\
x \neq 0 \\
\text { all real } x
\end{array}
\]
(c) Find a formula for \( f^{\prime} \) ',
\[
f^{\prime}(x)=\square x
\]

Let f(x)=x|x|.
(a) Skatch the graph of the function.
(1)
Oroace B
Oroace D
Contce C
Cumace
(1)
(b) For what values of x is f differentiable?

0 x ≥ 0

x<0

x>0

x ≠ 0
all real x

(c) Find a formula for f^' ',

f^'(x)=□ x

Added by Adam W.

Calculus Early Transcendentals

James Stewart 7th Edition

Chapter 2

Instant Answer

Solved by Expert Keerti J

Step 1

- The function \( f(x) = x|x| \) can be rewritten using the definition of absolute value: - If \( x \geq 0 \), then \( |x| = x \) and \( f(x) = x \cdot x = x^2 \). - If \( x < 0 \), then \( |x| = -x \) and \( f(x) = x \cdot (-x) = -x^2 \). - Therefore, \( f(x) Show more…

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Let \( f(x)=x|x| \). (a) Skatch the graph of the function. (1) Oroace B Oroace D Contce C Cumace (1) (b) For what values of \( x \) is \( f \) differentiable? \[ \begin{array}{l} 0 x \geq 0 \\ x<0 \\ x>0 \\ x \neq 0 \\ \text { all real } x \end{array} \] (c) Find a formula for \( f^{\prime} \) ', \[ f^{\prime}(x)=\square x \]