Chapter 10 Multiple choice questions

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. Which of the following is not true of z = f(x,y) ?

z is a function of two variables, x and y. correct incorrect

The partial derivative (∂z/∂x)_y gives the rate of change of z with respect to x when y is kept constant. correct incorrect

∂z/∂x)_y = (∂z/∂y)_x correct incorrect

The gradient of z is a 2-dimensional vector. correct incorrect

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. If the gradient of a function of three variables Ω = f(x,y,z) is 4i + 3k, what is the rate of change of Ω in the direction 2i + 2j – k ?

1 correct incorrect

5/3 correct incorrect

5 correct incorrect

15 correct incorrect

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. If z = x²y³ + ln(y), what is (∂y/∂x)_z?

-2xy⁴ / (3x²y³ + 1) correct incorrect

3xy³ / (2x²y² + 1) correct incorrect

2x²y³ / (x²y² + 3) correct incorrect

-3x²y³ / (x²y² + 2) correct incorrect

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. Which of the following is not true at a maximum point of z = f(x,y) ?

(∂z/∂x)_y = 0 and (∂z/∂y)_x = 0 correct incorrect

(∂²z/∂x²) (∂²z/∂y²) > (∂²z/∂x∂y)² correct incorrect

∂²z/∂x² + ∂²z/∂y² < 0 correct incorrect

It is the point where z takes the largest value possible. correct incorrect

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. If (∂²z/∂x²) (∂²z/∂y²) = (∂²z/∂x∂y)² at a stationary point, what is its nature?

Minimum. correct incorrect

Maximum. correct incorrect

Saddle point. correct incorrect

Not able to characterise the nature on the given information. correct incorrect