Question

Consider the function ‘f’ given by f(x) log x, x > 0, then the function ‘f’ is ______.

Options

• differentiable and continuous at x = 1.

• differentiable but not continuous x = 1.

• continuous but not differentiable at x = 1.

• Neither differentiable nor continuous at x = 1.

Answer 1

Consider the function ‘f’ given by f(x) log x, x > 0, then the function ‘f’ is differentiable and continuous at x = 1.

Explanation:

f(x) = logx, defined for x > 0

It is differentiable for all x > 0

Derivative: f(x) = `1/x`

At x = 1x: f′(1) = 1 → derivative exists

Since differentiability ⇒ continuity, the function is also continuous at x = 1