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GATE 2024 DA – Question 33

Calculus and Optimization · Limits, continuity and differentiability · 1 mark · Numerical answer

Let $f: \mathbb{R} \to \mathbb{R}$ be the function $f(x) = \frac{1}{1 + e^{-x}}$.

The value of the derivative of $f$ at $x$ where $f(x) = 0.4$ is ______ (rounded off to two decimal places).

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Correct answer: 0.23 to 0.25

Explanation

For the logistic function $f'(x) = f(x)(1 - f(x))$. At the point where $f = 0.4$ this is $0.4 \times 0.6 = 0.24$.