To find the integral of a function

To solve a quadratic equation

To find the differential of a function and compare it to the true change

To determine the maximum value of a function

Delta x = 0.5 and Delta y = -0.25

Delta x = -0.25 and Delta y = 0.5

Delta x = 0.25 and Delta y = 0.15

Delta x = -0.5 and Delta y = 0.25

(4.25, 1.5)

(3.5, 1.75)

(4.5, 1.25)

(3.75, 1.15)

By differentiating with respect to both x and y simultaneously

By integrating with respect to x

By treating y as a constant and differentiating with respect to x

By treating x as a constant and differentiating with respect to y

6x e^(3y)

2x e^(3y)

4x e^(3y)

3x e^(2y)

Partial derivative of f with respect to x times delta y

Partial derivative of f with respect to x times differential y plus partial derivative of f with respect to y times differential x

Partial derivative of f with respect to y times delta x

Partial derivative of f with respect to x times differential x plus partial derivative of f with respect to y times differential y

80.45678

50.12345

62.26516

75.56864

62.26516

75.56864

50.12345

80.45678

Because the function is linear

Because the changes in x and y are too large

Because the function is not continuous

Because the changes in x and y are too small

Calculating the integral instead

Using a different function

Decreasing the changes in x and y

Increasing the changes in x and y