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2 years ago

Can anyone help me with this math question please I will give brainlist!!

Mathematics

2 answers:

horrorfan [7]2 years ago

8 0

the other 2 coordinates are option C

guajiro [1.7K]2 years ago

5 0

Answer:

Ans is (4,2) and (5,4)

which lies nesr to coordinates 4,4 and 3,2 so option C

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Consider the following equation. f(x, y) = y3/x, P(1, 2), u = 1 3 2i + 5 j (a) Find the gradient of f. ∇f(x, y) = Correct: Your

BaLLatris [955]

$f(x,y)=\dfrac{y^3}x$

a. The gradient is

$\nabla f(x,y)=\dfrac{\partial f}{\partial x}\,\vec\imath+\dfrac{\partial f}{\partial y}\,\vec\jmath$

$\boxed{\nabla f(x,y)=-\dfrac{y^3}{x^2}\,\vec\imath+\dfrac{3y^2}x\,\vec\jmath}$

b. The gradient at point P(1, 2) is

$\boxed{\nabla f(1,2)=-8\,\vec\imath+12\,\vec\jmath}$

c. The derivative of $f$ at P in the direction of $\vec u$ is

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It looks like

$\vec u=\dfrac{13}2\,\vec\imath+5\,\vec\jmath$

so that

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Then

$D_{\vec u}f(1,2)=\dfrac{\left(-8\,\vec\imath+12\,\vec\jmath\right)\cdot\left(\frac{13}2\,\vec\imath+5\,\vec\jmath\right)}{\frac{\sqrt{269}}2}$

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