A differentiable function $f(x)$ is such that $f(-0.1) = 2$, $f(0) = 1$, and $f(0.1) = 2$. Then, $\dfrac{d^2f}{dx^2}$ at $x = 0$ is ______ (answer in integer).

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Step 1: Pick the right numerical formula. For a function known at three equally spaced points $x_0 - h$, $x_0$, $x_0 + h$, the second derivative is estimated using the central difference formula: $$ f''(x_0) \approx \frac{f(x_0+h) - 2f(x_0) + f(x_0-h)}{h^2} $$ Here $x_0 = 0$, $h = 0.1$, $f(-0.1) = 2$, $f(0) = 1$, $f(0.1) = 2$. Step 2: Substitute the values. $$ f''(0) \approx \frac{2 - 2(1) + 2}{(0.1)^2} = \frac{2}{0.01} $$ Step 3: Simplify. $\dfrac{2}{0.01} = 200$. Final Answer: The second derivative of $f$ at $x = 0$ works out to 200. $$ \boxed{200} $$

A differentiable function \(f(x)\) is such that \(f(-0.1) = 2\), \(f(0) = 1\), and \(f(0.1) = 2\).

Then, \(\dfrac{d^2f}{dx^2}\) at \(x = 0\) is ______ (answer in integer).

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Correct Answer: 200

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Top GATE NM Engineering Mathematics Questions

Top GATE NM Questions

A differentiable function \(f(x)\) is such that \(f(-0.1) = 2\), \(f(0) = 1\), and \(f(0.1) = 2\).Then, \(\dfrac{d^2f}{dx^2}\) at \(x = 0\) is ______ (answer in integer).