If the above function is differentiable, then the value of k + m is:

Question

Question

Answer 1

Concept:

A function g(x) is said to be differentiable at a point 'a', if:

Properties:

If a function is differentiable at any point, then it is necessarily continuous at the point.
But the converse of this statement is not true i.e. continuity is a necessary but sufficient condition for the Existence of a finite derivative.
Differentiability implies Continuity.
Continuity does not necessarily imply differentiability.

Any function f is said to be continuous at a point 'a', if and only if:

Analysis:

For 3^-, the function is:

For 3+, the function is:

g(x) = mx + 2

Since g(x) is differentiable, it will be continuous at x = 3, i.e.

2 k = 3 m + 2 ---(1)

Also, g(x) is differentiable at x = 0, i.e.

Equating the derivatives of both the functions for x = 3^- and x = 3⁺, we get:

Putting x = 3:

K = 4 m ---(2)

Solving (1) and (2), we get:

∴ k + m = 2

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