Suppose that z is a linear function of x and y with slope 2 in the x-direction and slope 3 in the y-direction. (a) a change of 0.5 in x and −0.1 in y produces what change in z?

Answer = 0.7

Solution -

Similar to linear functions of one variable, we have the Slopes - Intercept Formula for a linear function of two variables given by,

⇒ z  =  m₁x+m₂y+c

where

m₁ = slope in X direction = 2

m₂ = slope in Y direction = 3

c = c is the z-intercept of the plane defined by the equation.

Taking the derivatives of both sides

⇒ dz = m₁dx + m₂dy

dx = change in x = 0.5

dy = change in y = -0.1

Putting all the values in the equation

⇒ dz = 2×0.5 + 3(-0.1) = 0.7

Hence, change in z = 0.7

rx and sx

step-by-step explanation:

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x