M28 3.5.pptx - 3.5 Gradients and Directional derivatives...

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3.5 Gradients and Directional derivatives
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Review Given: : slope of the tangent line to the curve at the point y f x dy f' a dx y f x P a,f a
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Geometrically Given: : slope of the tangent line to the curve of intersection of and the plane at the point z f x,y x z f a,b x z f x,y P a,f a y b
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Geometrically Given: x z f a,b x x y z a b b , a f m x z f x,y y b
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Geometrically Given: : slope of the tangent line to the curve of intersection of and the plane at the point z f x,y y z f a,b y z f x,y P a,f a x a
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Geometrically Given: b , a f y z y x y z a b b , a f m y x a z f x,y
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Notion A directional derivative is a rate of change towards a particular direction.
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Directional derivative Given: x y z a b z f x,y
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unit vector in -direction:
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