Find the maximum rate of change of f(x,y) = x2y +2y

Mathematics

1 answer:

nevsk [136]3 years ago

4 0

Answer:

Maximum rate of change at the point (-1,2) = √17

Direction is the direction of the gradient

Step-by-step explanation:

The gradient of a function (scalar or vectorial ) is a vector in the direction of maximum rate of change then

f( x,y ) = x*2y + 2y

grad = δ/δx i + δ/δy j + δ/δz k

grad f(x,y) = [ δ/δx i , δ/δy] = [ 2y , x+2 ]

at the point ( -1 , 2 )

grad f(x,y) = [4 , 1]

| grad f(x,y) | = √ (4)² + (1)² = √17

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Answer:

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Step-by-step explanation:

Based on the histogram given :

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3 years ago

RoseWind [281]

Please note that dilation does not affect angles. Thus, if an image is dilated the angle remains the same and does not change.

Therefore, even if $\Delta ABC$ is dilated to $\Delta JKL$ by a factor of 1.5 (or by any factor for that matter), the linear dimensions of the original triangle $\Delta ABC$ will either get stretched or get shrunk by a factor of 1.5 but the angles of the original triangle will not be affected in any case.