Find the values of m and b

Question

Let g(x) = { x^ 2      x ≤ 3

                    mx+b    x > 3

Find the values of m and b such that f is continuous everywhere and differentiable at x = 3.

Answer 1

Step 1:

The function is .

The function is continuous and differentiable at x = 3.

A function is said to be continuous at x = a if and only if

Consider .

Consider .

The function is continuous at x = 3.

                          equation (1)

Step 2:

A function is said to be differentiable at x = a if and only if

Consider

Consider .

The function is differentiable at x = 3.

Step 3:

Substitute in equation (1).

Substitute and in the function .

Solution:

and .