Final answer:
For the function f(x) to be continuous from the right at x=2, the value of c must be ±1/2 to ensure the limit as x approaches 2 from the right is equal to f(2), which is 3.
Step-by-step explanation:
To determine for what value(s) of c the function f(x) is continuous from the right at x=2, we need to make sure that the limit of f(x) as x approaches 2 from the right is equal to f(2).
We are given that f(2) = 3, so for continuity from the right at x=2, the limit of the function f(x) as x approaches 2 from the right must also be equal to 3.
The function for x > 2 is c²x²+2. To find the limit as x approaches 2, we substitute x with 2:
c²(2)²+2 = c²·4+2 = 4c²+2.
To make the function continuous from the right at x=2, we set:
4c²+2 = 3
- 4c² + 2 = 3
- 4c² = 1
- c² = 1/4
- c = ±1/2
Therefore, the function is continuous from the right at x=2 when c is ±1/2.