Question

If the function f defined by f(x) = x^2 + 3x +a, x≤1 bx+2, x>1

Is derivable, then find the values of a and b.

Answer 1

For f(x) to be continuous at x = 1,
x² +3x +a = bx + 2 when x = 1. So, a + 4 = b + 2 ........eq1)

For f(x) to be differentiable when x = 1, the function must be continuous when x = 1 and the one-sided derivatives must be equal when x = 1.

So, 2x + 3 = b at x = 1. Thus, b = 5

putting the value of b at eq1)

a + 4 = b +2
a +4 = 5 +2
a = 3

Ans. a=3, b=5