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Show transcribed image text 3. In the video we stated that ▽f(20,30) points in the direction of greatest increase of f from the point (o,o. In this problem we will use geometry to see why this is true. Let f(x, y) be a function and (o, yo) be a point. a) Explain why the direction of greatest increase from P on f is the vector u for which Duf to,yo) is greatest. (b) Use an old formula to rewrite Duf(xo,yo) = ▽f(zo,yo) . u in terms of cos θ where θ is the angle between ▽f(xo, yo) and u. (c) Show that Duf(zo,yo) = llVf(zo,Yo)II cose. (d) The value of cos θ is greatest when cos θ = 1 . For what value of θ is that true? (e) Explains why this means that the directional derivative is the greatest in the same direction as ▽f(zo,yo).
3. In the video we stated that ▽f(20,30) points in the direction of greatest increase of f from the point (o,o. In this problem we will use geometry to see why this is true. Let f(x, y) be a function and (o, yo) be a point. a) Explain why the direction of greatest increase from P on f is the vector u for which Duf to,yo) is greatest. (b) Use an old formula to rewrite Duf(xo,yo) = ▽f(zo,yo) . u in terms of cos θ where θ is the angle between ▽f(xo, yo) and u. (c) Show that Duf(zo,yo) = llVf(zo,Yo)II cose. (d) The value of cos θ is greatest when cos θ = 1 . For what value of θ is that true? (e) Explains why this means that the directional derivative is the greatest in the same direction as ▽f(zo,yo).
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