4 Maths -- Applications of Derivatives

A stone is dropped into a quiet lake and waves move in the form of circles at a speed of 4 cm/sec. At the instant, when the radius of the circular wave is 10 cm, how fast is the enclosed area increasing?

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State Rolle's theorem. Verify that the function f(x)= x(x-3)^2 on [0,3] satisfies conditions of Rolle's theorem and find C prescribed in the theorem.

At what angle does the curve y(1+x)=x cut the x-axis?

The total cost C(x) associated with the production of x units of an item is given by C(x) = 0.005x3 – 0.02x2 + 30x + 5000. Find the marginal cost when 3 units are produced, where by marginal cost w...

The volume of a sphere is increasing at the rate of 8 cm3/s. Find the rate at which its surface area is increasing when the radius of the sphere is 12 cm.

For the given curve: y = 5x – 2x3, when x increases at the rate of 2 units/sec, then how fast is the slope of curve changes when x = 3?

Show that the function f(x) = tan x – 4x is strictly decreasing on [-π/3, π/3]

Determine all the points of local maxima and local minima of the following function: f(x) = (-¾)x4 – 8x3 – (45/2)x2 + 105

A circular disc of radius 3 cm is being heated. Due to expansion, its radius increases at a rate of 0.05 cm per second. Find the rate at which its area is increasing if the radius is 3.2 cm.

Determine the approximate variation in the surface area of a cube of side x metres caused by decreasing the side by 1%.

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4 Maths -- Applications of Derivatives

A stone is dropped into a quiet lake and waves move in the form of circles at a speed of 4 cm/sec. At the instant, when the radius of the circular wave is 10 cm, how fast is the enclosed area increasing?

0 Answers

More questions on Applications of Derivatives

State Rolle's theorem. Verify that the function f(x)= x(x-3)^2 on [0,3] satisfies conditions of Rolle's theorem and find C prescribed in the theorem.

At what angle does the curve y(1+x)=x cut the x-axis?

The total cost C(x) associated with the production of x units of an item is given by C(x) = 0.005x3 – 0.02x2 + 30x + 5000. Find the marginal cost when 3 units are produced, where by marginal cost w...

The volume of a sphere is increasing at the rate of 8 cm3/s. Find the rate at which its surface area is increasing when the radius of the sphere is 12 cm.

For the given curve: y = 5x – 2x3, when x increases at the rate of 2 units/sec, then how fast is the slope of curve changes when x = 3?

Show that the function f(x) = tan x – 4x is strictly decreasing on [-π/3, π/3]

Determine all the points of local maxima and local minima of the following function: f(x) = (-¾)x4 – 8x3 – (45/2)x2 + 105

A circular disc of radius 3 cm is being heated. Due to expansion, its radius increases at a rate of 0.05 cm per second. Find the rate at which its area is increasing if the radius is 3.2 cm.

Determine the approximate variation in the surface area of a cube of side x metres caused by decreasing the side by 1%.