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Find and classify the critical points of: $f(x,y)=3x+4y^2$

I started off by working out the partial derivatives for the gradient, which leaves me with

$\nabla f(x,y) = (3, 8y)$, and set equal to 0 so 3=0 which means the gradient for x doesn't exist, and 8y=0. This still means I have a critical point right? If I do, how do I classify it if I can't take a second derivative of it?

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The gradient exists everywhere, it's just never equal to $(0, 0)$. That is, your $f$ has no critical points.

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  • $\begingroup$ Ah ok I was a bit confused seeing that we have a y value and no x value. Thanks for the help! $\endgroup$ – Orangegulf Mar 10 '15 at 15:52

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