The question said we should find the rate of change of the function:
3x + y = 8
First let's differentiate each term with respect to the independent variable:
d/dx (3x) + d/dx (y) = d/dx (8)
Let's apply chain rule:
d/dx (3x) + dy/dx = d/dx (8)
Let's take out the coefficients:
3 * d/dx (x) + dy/dx = d/dx (8)
Let's differentiate the constant:
3 * d/dx (x) + dy/dx = 0
Apply power rule:
3 + dy/dx = 0
Let's differewntiate the implicit function:
dy/dx = -3
Therefore the rate of change of the function is -3.
So the correct option is the last option which is -3.