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0. Functions(0)

Introduction to Functions
(0)

Piecewise Functions
(0)

Properties of Functions
(0)

Common Functions
(0)

Transformations
(0)

Combining Functions
(0)

Exponent rules
(0)

Exponential Functions
(0)

Logarithmic Functions
(0)

Properties of Logarithms
(0)

Exponential & Logarithmic Equations
(0)

Introduction to Trigonometric Functions
(0)

Graphs of Trigonometric Functions
(0)

Trigonometric Identities
(0)

Inverse Trigonometric Functions
(0)

1. Limits and Continuity(0)

Introduction to Limits
(0)

Finding Limits Algebraically
(0)

Continuity
(0)

2. Intro to Derivatives(0)

Tangent Lines and Derivatives
(0)

Derivatives as Functions
(0)

Basic Graphing of the Derivative
(0)

Differentiability
(0)

3. Techniques of Differentiation(0)

Basic Rules of Differentiation
(0)

Higher Order Derivatives
(0)

Product and Quotient Rules
(0)

Derivatives of Trig Functions
(0)

The Chain Rule
(0)

4. Applications of Derivatives(0)

Motion Analysis
(0)

Implicit Differentiation
(0)

Related Rates
(0)

Linearization
(0)

Differentials
(0)

5. Graphical Applications of Derivatives(0)

Intro to Extrema
(0)

Finding Global Extrema
(0)

The First Derivative Test
(0)

Concavity
(0)

The Second Derivative Test
(0)

Curve Sketching
(0)

Applied Optimization
(0)

6. Derivatives of Inverse, Exponential, & Logarithmic Functions(0)

Derivatives of Exponential & Logarithmic Functions
(0)

Logarithmic Differentiation
(0)

Derivatives of Inverse Trigonometric Functions
(0)

7. Antiderivatives & Indefinite Integrals(0)

Antiderivatives
(0)

Indefinite Integrals
(0)

Integrals of Trig Functions
(0)

Initial Value Problems
(0)

8. Definite Integrals(0)

Estimating Area with Finite Sums
(0)

Riemann Sums
(0)

Introduction to Definite Integrals
(0)

Fundamental Theorem of Calculus
(0)

Average Value of a Function
(0)

Substitution
(0)

9. Graphical Applications of Integrals(0)

Area Between Curves
(0)

Introduction to Volume & Disk Method
(0)

10. Physics Applications of Integrals (0)

Kinematics
(0)

Work
(0)

11. Integrals of Inverse, Exponential, & Logarithmic Functions(0)

Integrals of Exponential Functions
(0)

Integrals Involving Logarithmic Functions
(0)

Integrals Involving Inverse Trigonometric Functions
(0)

12. Techniques of Integration(0)

Integration by Parts
(0)

Partial Fractions
(0)

Improper Integrals
(0)

13. Intro to Differential Equations(0)

Basics of Differential Equations
(0)

Slope Fields
(0)

Euler's Method
(0)

Separable Differential Equations
(0)

14. Sequences & Series(0)

Sequences
(0)

Review of Factorials
(0)

Series
(0)

Convergence Tests
(0)

15. Power Series(0)

Introduction to Power Series
(0)

Taylor Series & Taylor Polynomials
(0)

16. Parametric Equations & Polar Coordinates(0)

Parametric Equations
(0)

Calculus with Parametric Curves
(0)

Polar Coordinates
(0)

Calculus in Polar Coordinates
(0)

Conic Sections
(0)

5. Graphical Applications of Derivatives

Applied Optimization

5. Graphical Applications of Derivatives

Applied Optimization: Videos & Practice Problems

Video Lessons Practice Worksheet

Back to all problems

Back to all problems

82 of 0

Problem 82Multiple Choice

A city park is designing a decorative sign in the shape of a rectangle topped by a semicircle. The rectangular portion is made of clear acrylic, while the semicircular top is made of frosted acrylic, which allows only one-third as much light through per unit area as the clear portion. The total perimeter of the sign is fixed. Let $r$ be the radius of the semicircle and $h$ be the height of the rectangular portion. Determine the ratio of $r$ to $h$ that will allow the most light to pass through. Neglect the thickness of the sign.

A

$\frac{3}{2 + 3 π}$

B

$\frac{3}{3 + 2 π}$

C

$\frac{3}{3 + π}$

D

$\frac{3}{1 + 3 π}$

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