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In: Math

Let f(x, y) = − cos(x + y2 ) and let a be the point a...

Let f(x, y) = − cos(x + y2 ) and let a be the point a = ( π/2, 0).

(a) Find the direction in which f increases most quickly at the point a.

(b) Find the directional derivative Duf(a) of f at a in the direction u = (−5/13 , 12/13) .

(c) Use Taylor’s formula to calculate a quadratic approximation to f at a.

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