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

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Basic Math

T/F and why(true/false)?

(Part a) If the partial derivatives fx(x,y),fy(x,y) exists for all values x,y ,then f(x,y) iscontinuous.

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

,f(x,y) ? 0, f(0,0) = 0.Then the gradient vector is zero at theorigin is,?f(0,0) = (0,0).

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

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

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