**Problem:** Find the directional derivative of the function \( f(x, y) = x^2 + y^2 \) at the point \((2, 1)\) in the direction \(\langle 1, 1 \rangle\). **Options:** A) \( \frac{3}{\sqrt{2}} \) B) \( \frac{7}{\sqrt{2}} \) C) \( 7 \) D) \( 3 \) E) None of these

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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**Problem:**

Find the directional derivative of the function \( f(x, y) = x^2 + y^2 \) at the point \((2, 1)\) in the direction \(\langle 1, 1 \rangle\).

**Options:**

A) \( \frac{3}{\sqrt{2}} \)

B) \( \frac{7}{\sqrt{2}} \)

C) \( 7 \)

D) \( 3 \)

E) None of these
Transcribed Image Text:**Problem:** Find the directional derivative of the function \( f(x, y) = x^2 + y^2 \) at the point \((2, 1)\) in the direction \(\langle 1, 1 \rangle\). **Options:** A) \( \frac{3}{\sqrt{2}} \) B) \( \frac{7}{\sqrt{2}} \) C) \( 7 \) D) \( 3 \) E) None of these
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