Class 12 Maths: Application of Derivatives Basics

1. Q1. The slope of the tangent to the curve y = f(x) at a point (x₀, y₀) is given by:
   • f(x₀)
   • f'(x₀)
   • y₀
   • dy/dx
2. Q2. 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:
   • f'(x) < 0
   • f'(x) = 0
   • f'(x) > 0
   • f'(x) ≤ 0
3. Q3. The rate of change of the area of a circle with respect to its radius r, when r = 5 cm, is:
   • 5π cm²/cm
   • 10π cm²/cm
   • 25π cm²/cm
   • 2π cm²/cm
4. Q4. 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?
   • dy/dx is undefined
   • dy/dx = 1
   • dy/dx = 0
   • dy/dx > 0
5. Q5. 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:
   • f'(x)
   • -1/f'(x)
   • 1/f'(x)
   • -f'(x)

+ 5 more in the printable PDF.