What is the Gradient of a Function at a Given Point?

[JProgrammer]

I am trying to find the direction of steepest ascent of this function with this given point:

f(x) = x^2 - 4y^2 - 9

(1,-2)

I have the understanding that the steepest ascent or in some cases descent can be measured by the gradient. So in wolfram alpha I type in: gradient f(x) = x^2 - 4y^2 - 9, (1,-2) it says it interprets my input as: grad(-9+x^2-4 y^2, 18+x^2-4 y^2)
and gives me: grad(-9+x^2-4 y^2, 18+x^2-4 y^2) = ({2 x, 2 x}, {-8 y, -8 y}).

It interprets my input wrong and does not give me a direction. If someone could tell me what I am doing wrong and what I need to do instead, I would appreciate.

Thank you.

 

[Greg]

Shouldn't that be f(x, y)?

 

[topsquark]

I am trying to find the direction of steepest ascent of this function with this given point:

f(x) = x^2 - 4y^2 - 9

(1,-2)

I have the understanding that the steepest ascent or in some cases descent can be measured by the gradient. So in wolfram alpha I type in: gradient f(x) = x^2 - 4y^2 - 9, (1,-2) it says it interprets my input as: grad(-9+x^2-4 y^2, 18+x^2-4 y^2)
and gives me: grad(-9+x^2-4 y^2, 18+x^2-4 y^2) = ({2 x, 2 x}, {-8 y, -8 y}).

It interprets my input wrong and does not give me a direction. If someone could tell me what I am doing wrong and what I need to do instead, I would appreciate.

Thank you.

Really? I got this. But it's so simple a problem, why are you using W|A to do it? Do you know how to take the gradient?

-Dan