List of top Mathematics Questions on Application of derivatives asked in CUET (UG)

The rate of change of area of a circle with respect to its circumference when radius is 4cm, is
If the maximum value of the function f(x) = $\frac{\log_e x}{x}$, x > 0 occurs at x = a, then a2f''(a) is equal to
The total cost C(x) in Rupees associated with the production of x units of an item is given by C(x) = \(0.007x^3 - 0.003x^2 + 15x + 400\). The marginal cost when 10 items are produced is:
The total cost C(x) in Rupees associated with the production of x units of an item is given by C(x) = \(0.007x^3 - 0.003x^2 + 15x + 400\). The marginal cost when 10 items are produced is:
The rate of change of area of a circle with respect to its circumference when radius is 4cm, is
The function f(x) = tanx - x

Match List-I with List-II

List-IList-II
(A) The minimum value of \( f(x) = (2x - 1)^2 + 3 \)(I) 4
(B) The maximum value of \( f(x) = -|x + 1| + 4 \)(II) 10
(C) The minimum value of \( f(x) = \sin(2x) + 6 \)(III) 3
(D) The maximum value of \( f(x) = -(x - 1)^2 + 10 \)(IV) 5


Choose the correct answer from the options given below:

The interval, on which the function f(x) = x2e-x is increasing, is equal to
The slope of the normal to the curve y = \(2x^2\) at x = 1 is:
The slope of the normal to the curve y = \(2x^2\) at x = 1 is:
If the maximum value of the function f(x) = $\frac{\log_e x}{x}$, x > 0 occurs at x = a, then a2f''(a) is equal to
The function f(x) = tanx - x

Match List-I with List-II

List-IList-II
(A) The minimum value of \( f(x) = (2x - 1)^2 + 3 \)(I) 4
(B) The maximum value of \( f(x) = -|x + 1| + 4 \)(II) 10
(C) The minimum value of \( f(x) = \sin(2x) + 6 \)(III) 3
(D) The maximum value of \( f(x) = -(x - 1)^2 + 10 \)(IV) 5


Choose the correct answer from the options given below:

The interval, on which the function f(x) = x2e-x is increasing, is equal to