# Find the gradient of a function at a given point, sketch level curve

#### skatenerd

##### Active member
So I have a function $$f(x,y)=\sqrt{2x+3y}$$ and need to find the gradient at the point (-1,2). I got this part already, its $$\frac{1}{2}\hat{i}+\frac{3}{4}\hat{j}$$. The part I'm having trouble with is when it asks me to sketch the gradient with the level curve that passes through (-1,2).
The back of the book has the answer and it calls the line passing through the point given point $$4=2x+3y$$. I know that in relation to the given function this would also equal $$2=\sqrt{2x+3y}$$. So where does that 2 come from?

#### MarkFL

$f(-1,2)=\sqrt{2(-1)+3(2)}=\sqrt{4}=2$