Revision on Differentiation

Give two real-life applications of differentiation.

Answer explanation

Use of chain rule when differentiating.

The diagram shows the curve with equation y = a ln x − 4x, where a is a positive constant. Find, in terms of a, an equation for the tangent to the curve at the point where x = 1.

Answer explanation

First, find dy/dy and then find the stationary point, obtaining x and y. Finally use y=mx+c to find the equation.

Explain how you would use differentiation to determine the nature of a stationary point.

Answer explanation

Use of second derivatives. If the second derivative is greater than 0, the stationary point is a minimum point. If it is less than 0, the stationary point is a maximum point.

• t=9

• t=6

• t=3

• t=-1

Answer explanation

The object will not be moving if the velocity is ever zero and so all we need to do is set the derivative equal to zero and solve.

s′(t)=0

12t(t−3)(t−7)=0

Hence, the object will not be moving, at t=0, t=3, t=7.

Answer explanation

Use Quotient Rule as one function is divided by another.