# Transcribed Image Text: Let f(z, y) be a scalar function

Transcribed Image Text: Let f(z, y) be a scalar function. Which of the following statements are true? Select all that apply.

O If f is not differentiable at a point (a, b), then f is not continuous at (a, b).

O If f, and f, do not exist at (a, b), then f is not differentiable at (a, b).

O If f, and f, exist at (a, b), then f is differentiable at (a, 6).

O If f is continuous at a point (a, b), then f is differentiable at (a, b).

O None of the above.

The height of a mountain at point (x, y) is given by h(x, y) = xe-y + 5x. You are standing on the mountain

above the point (1,1). From your position, which of the following statements are true? Select all that apply.

O The slope of the path of steepest ascent is equal to 50.

O The height is increasing most rapidly in the direction of (-1,7).

O The equation of the tangent line at the point (1,1) to the level curve h(z, y) = 6 is

7(2 – 1) – (y – 1) = 0.

O The height is decreasing most rapidly in the direction of (-7,1).

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