Understanding Derivative Functions and Direction Fields

To solve a system of equations

To find the slope of a line

To determine which derivative function produces a given direction field

To calculate the area under a curve

They have undefined slopes

They are not on the coordinate plane

Their derivative function values are zero

They are too complex to calculate

(0, 1)

(0, 0)

(1, 0)

(1, 1)

The derivative function value is zero

The derivative function value does not match the slope

The derivative function value is positive

The derivative function value matches the slope

dydx = x * y

dydx = x^2 * y^2

dydx = y^2 * x

dydx = x * y^2

It has no effect on the direction field

It is the correct function

It is eliminated due to incorrect slopes

It matches the direction field

dydx = x^2 * y^2

dydx = x * y

dydx = x * y^2

dydx = y^2 * x

It is not a valid function

It matches the direction field

It produces positive slopes at all points

It produces negative slopes

Zero

Negative 1

Positive 1

Undefined

Trial and error

Graphical analysis

Process of elimination

Algebraic manipulation