Practice Examples on Applications of Derivatives
Example 1: Find the rate of change of the area of a circle with respect to its radius r when r = 6 cm.
Example 2: Find the equation of a tangent to the curve y=x4–6×3+13×2–10x+5 at the point (1, 3).
Example 3: Amongst all the pairs of positive numbers with sum 24, find those whose product is maximum.
Example 4: Find the Stationary point of the function f(x)=x2−x+6.
Example 5: An edge of a variable cube is increasing at the rate of 5 cm/sec. How fast is the volume of the cube increasing when the edge is 10 cm long?
Example 6: The length x of a rectangle is decreasing at the rate of 5 cm/minute and the width y is increasing at the rate 4 cm/minute. When x = 8 cm and y = 6 cm then find the rate of change of the area of the rectangle.
Example 7: A spherical soap bubble is expanding so that its radius is increasing at the rate of 0.02 cm/sec. At what rate is the surface area is increasing when its radius is 5 cm? (Take π = 3.14).
Example 8: A stone is dropped into a quite pond and the waves moves in circles. If the radius of the circular wave increases at the rate of 8 cm/sec, find the rate of increase in its area at the instant when its radius is 6 cm?
Example 9: Find the rate of change of the area of a circle with respect to its radius r when r = 6 cm.
Example 10: If radius of circle is increasing at rate 0.5 cm/sec what is the rate of increase of its circumference?
Example 11: Find the Stationary point of the function f(x)=x2−x+8.
Example 12: Find the rate of change of the area of a circle with respect to its radius r when r = 9 cm.
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Practice Questions on Applications of Derivatives
In this article, we are going to see solved questions and also practice questions for a better understanding of the concept of the applications of derivatives.