Same chapter3 marksDifficulty: Medium
Find the maximum and minimum values of f(x) = x3 − 6x2 + 9x + 5.
Applications of Derivatives
4 marksDifficulty: Hard
A rectangle is to be made with a perimeter of 40 cm. Find the dimensions that give the greatest area.
Original Khojo Papers practice question — not from a past board paper.
Answer
A square of side 10 cm, with an area of 100 cm2.
No citable source has been recorded for this record. Treat it as practice material, not as fact.
Explanation
If one side is x the other is 20 − x, so the area is A = 20x − x2. Then dA/dx = 20 − 2x, which vanishes at x = 10, and the second derivative is negative, so the area is greatest there.
Related questions
From the same topic and chapter, at a similar level.
Same chapter3 marksDifficulty: Medium
The radius of a circle is increasing at 3 cm per second. Find the rate at which its area is increasing when the radius is 10 cm.
Applications of Derivatives
Same chapter3 marksDifficulty: Medium
Find the equation of the tangent to the curve y = x2 at the point (2, 4).
Applications of Derivatives
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Find the intervals in which f(x) = x3 − 3x is increasing and decreasing.
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Find the minimum value of f(x) = x + 1/x for x > 0.
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Same chapter3 marksDifficulty: Medium
Use differentials to find the approximate value of √36.6.
Applications of Derivatives