Linearization and Optimization Concepts

Create a model and picture of the problem.

Solve for the variable.

Find the derivative of the function.

Set the derivative equal to zero.

x + y = 179

2x + 2y = 179

x^2 + y^2 = 179

x * y = 179

x * y

x^2 + y^2

2x + 2y

x + y

By using the perimeter equation.

By setting the derivative of the surface area equation to zero.

By maximizing the volume.

By equating the surface area to the volume.

Marginal revenue is unrelated to marginal cost.

Marginal revenue equals marginal cost.

Marginal revenue is greater than marginal cost.

Marginal revenue is less than marginal cost.

L(x) = f(a) - f'(a)(x - a)

L(x) = f(a) + f'(a)(x - a)

L(x) = f(a) * f'(a)(x - a)

L(x) = f(a) / f'(a)(x - a)

By solving the function for zero.

By using a tangent line to approximate near a point.

By finding the exact value of the function.

By calculating the derivative at multiple points.

To find the maximum value of a function.

To find the minimum value of a function.

To find zeros of functions.

To approximate derivatives.