Class 12 Maths: Application of Derivatives Basics
Answer the questions and tap Submit to see your score. Your progress is auto-saved on this device.
Jump to question
Q1 · MCQ · 1 mark
The slope of the tangent to the curve y = f(x) at a point (x₀, y₀) is given by:
Q2 · MCQ · 1 mark
If a function f(x) is strictly increasing on an interval (a, b), then for all x ∈ (a, b), its derivative f'(x) must be:
Q3 · MCQ · 1 mark
The rate of change of the area of a circle with respect to its radius r, when r = 5 cm, is:
Q4 · MCQ · 1 mark
If the tangent to the curve y = f(x) at a point is parallel to the x-axis, then at that point, which of the following is true?
Q5 · MCQ · 1 mark
A normal to the curve y = f(x) is a line perpendicular to the tangent at the point of contact. The slope of the normal is:
Q6 · FILL · 1 mark
The interval on which the function f(x) = x² is strictly decreasing is ____.
Q7 · FILL · 1 mark
If the radius of a sphere is increasing at the rate of 2 cm/s, then the rate of change of its surface area when its radius is 3 cm is ____ cm³/s.
Q8 · FILL · 1 mark
The equation of the tangent to the curve y = x³ at the origin is ____.
Q9 · SHORT · 2 marks
Find the slope of the tangent to the curve y = 2x² - 3 at x = 1.
Q10 · SHORT · 2 marks
Explain the condition for a function to be strictly decreasing in an interval.