Revision Quiz (Maxima & Minima)

The maximum or minimum point are called the turning or stationary point.

• True

• False

For Maximum point : (i)  $\frac{\text{d}x}{\text{d}y}=0$ ; (ii)  $\frac{d^2y}{dx^2}$  < 0

• False

• True

For minimum point : (i)  $\frac{\text{d}x}{\text{d}y}=0$ ; (ii)  $\frac{d^2y}{dx^2}\ >\ 0$  

• False

• True

The critical points of the function  $f\left(x\right)=x^3-3x^2+7$  are

• 0, 2

• 0, -2

• 1, 2

• 2, -2

Maximum value of the function $f\left(x\right)=\left(x-2\right)^2+1$ is 

• 1

• 3

• 2

• none of these

Minimum value of the function $f\left(x\right)=4x^2-4x+1$ is 

• 0

• 1/2

• no minimum value

• none of these

Find the stationary points of the function f(x) = 3x^2 - 12x + 5.

• The stationary points are x = 4 and x = 3

• The stationary points are x = 5 and x = -2

• The stationary points are x = 2 and x = 2/3.

• The stationary points are x = 0 and x = 1

Determine the minima and maxima of the function g(x) = 2x^3 - 9x^2 + 12x - 4.

• The minima is at x = 1 and the maxima is at x = 3

• The minima is at x = -1 and the maxima is at x = 5

• The minima is at x = 2 and the maxima is at x = 4

• The minima is at x = 0 and the maxima is at x = 2

Use derivatives to find the critical points of the function f(x) = 3x^3 - 9x^2 + 6x - 2.

• f'(x) = 3x^2 - 9x + 6

• f'(x) = 6x^2 - 18x + 9

• f'(x) = 9x^2 - 18x + 6

• f'(x) = 9x^2 - 6x + 6

Calculate the critical points of the function g(x) = 4x^3 - 12x^2 + 8x - 3.

• The critical points are x = 3 and x = 5

• The critical points are x = 0 and x = 4

• The critical points are x = 2 and x = -1

• The critical points are x = 1 and x = 1/2.