Consider the function given by , , then the function 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
AIWritten by AI (gemini-2.5-pro) - it can contain mistakes.
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 $x = 1$.
From ISC 2026 Mathematics Paper 1, question 1(ii).