LEARN · EXPLAIN · REVISE

A tank volume V(h)=3h². Find dV/dh at h=t.

Read the idea, work independently, then explain what changed.

TOPIC 01

Derivatives and their applications: mixed review

A mixed assessment: identify the method, justify it and revise your reasoning.

Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Transfer#Your turn

t=32

The difference quotient uses h≠0; differentiability requires a finite common two-sided limit.

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Differentiate the specified function and substitute only after differentiating.

Hint 2

Use this intermediate relation.

dV/dh=6h

Worked solution

Differentiate the specified function and substitute only after differentiating.
Apply the stated relation and retain its conditions.
$V'(32)=192$
The derivative is volume change per height change, not necessarily volume change per time.

The requested value is 192.

Checks and common pitfalls: The derivative is volume change per height change, not necessarily volume change per time.

Think first. Reveal a hint when the class is ready.

Teacher preparation and assessment