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10.11.2019 •
Mathematics
Consider the function f (x comma y )equals3 x squared minus 2 y squared minus 3 and the point (negative 2 comma 1 ). a. find the unit vectors that give the direction of steepest ascent and steepest descent at p. b. find a vector that points in a direction of no change in the function at p.
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Ответ:
see description
Step-by-step explanation:
given the function![f(x,y) = 3x^2-2y^2-3](/tpl/images/0367/5108/e79d0.png)
we calculate the gradient![\nabla f(x,y) = \frac{\partial f(x,y)}{\partial x} \hat{\textbf{x}}+ \frac{\partial f(x,y)}{\partial y} \hat{\textbf{y}} + \frac{\partial f(x,y)}{\partial z} \hat{\textbf{z}}](/tpl/images/0367/5108/9bab9.png)
for each term we consider all variables different to the one we are derivating as constants. For each term we have
Therefore:
gives the direction of maxium increase.
a) with x = -2, y= 1
so the unitary vector in the direction of the steepest ascent is
and the unitary vector in the direction of steepest descent is
finally, the vector in no change direction is basically doing one of the following possibilities with
:
if we have a vector <a,b> the perpendicular vector (direction of no change) will be either <-a,b> or <a,-b>
so i will select <-a,b>
Ответ:
use photomath i help me a lot with math expressions
Step-by-step explanation: