CUET UG · Mathematics / Applied Mathematics (Domain)
Rate of change, increasing / decreasing functions, tangents and normals, maxima and minima.
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Q1 · Applications of Derivatives · EASY
The radius of a circular disc is increasing at the rate of 0.5 cm/s. At what rate is the area of the disc increasing when its radius is 10 cm?
Q2 · Applications of Derivatives · MEDIUM
Find the equation of the tangent to the curve y = x³ - 3x² + 2 at the point where x = 2.
Q3 · Applications of Derivatives · MEDIUM
The function f(x) = 2x³ - 9x² + 12x + 4 is strictly increasing in which interval?
Q4 · Applications of Derivatives · HARD
A wire of length 36 cm is bent to form a rectangle. What is the maximum possible area of the rectangle?
Q5 · Applications of Derivatives · EASY
The slope of the tangent to the curve y = x³ - 3x + 5 at the point (1, 3) is: