Differential Equations and Linear Functions

The video tutorial explores solving a differential equation with given initial conditions. It examines whether the function has a relative minimum or maximum at a specific point by evaluating the derivative. The tutorial then finds the constants m and b for which y=mx+b is a solution to the differential equation, and verifies the solution using a slope field.

What is the initial condition given for the differential equation?

• f(2) = 3

• f(1) = 0

• f(3) = 2

• f(0) = 1

What must be true about the derivative at a point for it to be a candidate for a relative minimum or maximum?

• The derivative must be undefined.

• The derivative must be zero.

• The derivative must be negative.

• The derivative must be positive.

What is the value of f'(2) in the given problem?

• 3

• 0

• 1

• 2

What is the form of the linear solution being considered for the differential equation?

• y = nx + c

• y = cx + d

• y = mx + b

• y = ax + b

What is the derivative of y = mx + b with respect to x?

• 0

• m

• x

• b

What is the value of the second derivative of a linear function?

• m

• x

• b

• 0

What is the value of m for the linear solution to the differential equation?

• 1

• 2

• 3

• 4

What is the value of b in the solution y = 2x - 2?

• 2

• 4

• 0

• -2

What is the y-intercept of the line y = 2x - 2?

• 1

• 0

• -2

• 2

What is the slope of the line y = 2x - 2?

• 3

• 2

• 4

• 1