Application of Differentiation

Stationary point occur when....

• x = 0

• $\frac{\text{d}y}{\text{d}x}=0$
  

• $\frac{\text{d}x}{\text{d}y}=0$

• $\frac{d^2y}{dx^2}=0$

The nature of stationary point for a curve   $y=x^2+2x-4$  is:

• inflection point

• minimum point

• intersection point

• maximum point

The nature of stationary point for a curve   $y=9-6x-x^2$  is:

• inflection point

• minimum point

• intersection point

• maximum point

Inflection point is a nature for stationary point when...

• $\frac{d^2y}{dx^2}<0$

• $\frac{d^2y}{dx^2}>0$

• $\frac{d^2y}{dx^2}=0$

• $\frac{d^2y}{dx^2}\ne0$

A rectangle whose sides 2x and x respectively changing at the rate of 0.5cm/s. Find the rate of change of its area when x= 2cm

• 5

• 4

• 6

• 3