Greetings,

CASE BASED QUESTIONS :

Suppose a car is travelling around the hill, and the path car follows along the hill is represented as y = 𝑥³ -3𝑥²+2. 

1. Determine the continuity of the function at x = 3?
(a) Continuous and value is 3
(b) Continuous and value is 2
(c) not continuous
(d) data insufficient

2. When the car follows the path from x= 2 to x = 1, then what is the change in the slope of the path of the hill?
(a) Increases
(b) decreases
(c) no change
(d) cannot be determined

3. When the car is at the instant (0, 2), suddenly landslide starts and on applying brakes the car slides tangentially. What is the equation of the path in which the car slides?
(a) x = 2
(b) y = 2
(c) x + y =2
(d) x – y = 2

4. When the car is at the instant (2,-2), the driver realised some slippery material like oil is spilled on the road. The driver applied brakes but the car slides normal at the instant. Find the equation of the normal path car took.
(a) x = 2
(b) y = 2
(c) x + y =2
(d) x – y = 2

5. What is the maximum value the path of the curve reaches in the domain [-1, 2] :
(a) 0
(b) 1
(c) 2
(d) 3

Please explain all the questions' answers with steps.
Regards,

NNABS