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on, partially because I do not know where to begin and partially

because I believe I dont even fully understand the problem. I

was wondering if any of you would be kind enough to show me what to

do? Thank you.

1. Suppose f(x,y) is differentiable for all (x,y), f(x,y)=17 on the

unit circle x^2+y^2=1 and grad f is never zero on the unit circle. For

any real number K, find a unit vector parallel to grad

f(cos(k),sin(k))....grad f stands for the gradient of f. But isnt it contradicting what its saying? It says f(x,y)=17 on the unit circle x^2+y^2. How the...?

I'm just supposing f(x,y) is differentiable for all (x,y), f(x,y)=17 on the unit circle x^2+y^2=1 and grad(f) is never zero on the unit circle(?) So you just find a unit vector parallel to grad f(cos(k),sin(k)), for k real, right?

PS- Do level curves apply to this problem?