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Choose the correct option.
Consider the function f given by f(x) = log x, x > 0, then the function f is:
Consider the function $f$ given by $f(x) = \log x$, $x > 0$, then the function $f$ is:
- adifferentiable and continuous at $x = 1$.
- bdifferentiable but not continuous at $x = 1$.
- ccontinuous but not differentiable at $x = 1$.
- dneither differentiable nor continuous at $x = 1$.
Answer
Answer
Correct option: a
Answer: (a) differentiable and continuous at $x = 1$.
The logarithmic function $f(x) = \log x$ is differentiable for all $x > 0$ with derivative $f'(x) = 1/x$. Since differentiability implies continuity, $f$ is both continuous and differentiable at $x = 1$.