T/F and why(true/false)? (Part a) If the partial derivatives fx(x,y), fy(x,y) exists for all values x,y...

T/F and why(true/false)?

(Part a) If the partial derivatives f_x(x,y), f_y(x,y) exists for all values x,y ,then f(x,y) is continuous.

(Part b) Suppose f(x,y) is a function which is differentiable and nonnegative everywhere, and is zero at the origin

,f(x,y) ≥ 0, f(0,0) = 0.Then the gradient vector is zero at the origin is,∇f(0,0) = (0,0).

(Part c) If F(x,y) is continuous on the entire plane, then there is a function f:R→R satisfying

f′(x) =F(x,f(x)), f(0) = 0 for all x∈R.

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milcah answered 1 year ago

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