Let $f ( x ) = x \left| x ^ { 3 } \right|$

question 11

Essay

Let $f ( x ) = x \left| x ^ { 3 } \right|$ .
a. Sketch the graph of $f$ .
b. For what values of $x$ is $f$ differentiable?
c. Find a formula for $f ^ { \prime } ( x )$ .

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Definitions:

Intellectual Ability

The capacity to perform mental activities—thinking, reasoning, and problem-solving—at a high level of complexity and efficiency.

People and Social Systems

Refers to the interrelationship between individuals and the societal structures in which they operate, highlighting how social, cultural, and institutional factors influence human behavior and interactions.

Creative Ability

The capacity to conceive and implement new and original ideas, solutions, or artistic expressions, reflecting innovation and unconventional thinking.

Competency-based Approach

A method that assesses individuals' skills and abilities, focusing on what they can do rather than what they know, often used in education and HR.