jimmyrepin

1. As x approaches 1,  f(x) approaches  3-1,  that is 2.

If a = 2 and b = 3,   f(1) = 2(1)^2 + 3(1)  = 5

So there is a 'jump' in values of x at x = 1.  So its not continuous at x=1.

2.  For continuity  at x = 1, ax^2  + bx must = 2  that is when a + b = 2.

3. for continuity at x = 2 , ax^2 + bx  must be = 0 that is when a*2^2 + 2b = 0

- that is 4a + 2b = 0.

4. we have system of equations:-

a + b = 2
4a + 2b = 0 

this gives a = -2 and b = 4   So  f(x) is continuous when a = -2 and b = 4.