A potter made a mud vessel, where the shape of the pot is based on f(x) = |x – 3| + | x - 2|, where f(x) represents the height of the pot.

Question

1. When x > 4 What will be the height in terms of x ?

a. x – 2

b. x -3

c. 2x -5

d. 5 – 2x

2. Will the slope vary with x value?

a. Yes

b. No

3. What is \(\cfrac{dy}{dx}\) at x = 3

a. 2

b. -2

c. Function is not differentiable

d. 1

4. When the x value lies between (2, 3) then the function is

a. 2x - 5

b. 5 – 2x

c. 1

d. 5

5. If the potter is trying to make a pot using the function f(x) = [x] ,will he get a pot or not? Why?

a. Yes, because it is a continuous function

b. Yes, because it is not continuous

c. No , because it is a continuous function

d. No , because it is not continuous

Answer 1

1. c) 2x - 5

2. a) yes

3. c) function is not differentiable

4. c) 1

5. d) No, because it is not continuous

Answer 2

1. (c) 2x - 5

For x > 4, 

f(x) = 2x - 5

2. (a) Yes

Since Slope changes as value of x changes.

3. (c) Function is not differentiable

Since on left and right side of x = 3, value of f'(x) is different it implies that the Function is not differentiable.

4. (c) 1

For 2 < x < 3

f(x) = 1

5. (d) No, because it is not continuous

f(x) = [x] = Greatest Integer Function

And, Greatest Integer Function is not continuous.