Applications of differentiation

Question 1 of 10

The equation of the tangent to y = x² at (1, 1) is

Question 2 of 10

The volume of a cube of side x is changing. dV/dx when x = 3 is

Question 3 of 10

If y = x³, find the rate of change of y when x = 2.

Question 4 of 10

A stationary point is a maximum if d²y/dx² is

Question 5 of 10

The stationary point of y = x² − 6x + 5 is

Question 6 of 10

At what value of x does y = x² − 6x + 5 have a stationary point?

Question 7 of 10

A rectangle has perimeter 40 cm. Its maximum possible area is

Question 8 of 10

A particle moves so that s = t³ − 2t. Find its velocity at t = 2.

Question 9 of 10

The minimum value of y = x² − 4x + 7 is

Question 10 of 10

The radius of a circle increases at 2 cm/s. How fast is its area increasing when r = 5 cm?