LEARN · EXPLAIN · REVISE

Find the minimum of x+t²/x for x>0.

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=34

A critical point needs a sign or second-derivative check; closed-interval global extrema also require endpoints.

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.

f\prime(x)=1-t^2/x^2

Worked solution

The requested value is 68.

Checks and common pitfalls: The negative critical solution is outside the positive domain.

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

Teacher preparation and assessment