Table of contents

0. Functions7h 52m
1. Limits and Continuity2h 2m
2. Intro to Derivatives1h 33m
3. Techniques of Differentiation3h 18m
4. Applications of Derivatives2h 38m
5. Graphical Applications of Derivatives6h 2m
6. Derivatives of Inverse, Exponential, & Logarithmic Functions2h 37m
7. Antiderivatives & Indefinite Integrals1h 26m
8. Definite Integrals4h 44m
9. Graphical Applications of Integrals2h 27m
- Area Between Curves
  1h 18m
- Introduction to Volume & Disk Method
  1h 8m
10. Physics Applications of Integrals 3h 16m
- Kinematics
  1h 13m
- Work
  2h 3m
11. Integrals of Inverse, Exponential, & Logarithmic Functions2h 34m
12. Techniques of Integration7h 39m
13. Intro to Differential Equations2h 55m
14. Sequences & Series5h 36m
15. Power Series2h 19m
- Introduction to Power Series
  1h 9m
- Taylor Series & Taylor Polynomials
  1h 10m
16. Parametric Equations & Polar Coordinates7h 58m

5. Graphical Applications of Derivatives

Finding Global Extrema

Calculus

5. Graphical Applications of Derivatives

Finding Global Extrema

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Multiple Choice

What is the end behavior of the graph of the polynomial function $y = 10 x^{9} - 4 x$ ?

x

approaches both

\infty

and

- \infty

y

approaches

\infty

x

approaches

\infty

y

approaches

\infty

; as

x

approaches

- \infty

y

approaches

- \infty

x

approaches both

\infty

and

- \infty

y

approaches

- \infty

x

approaches

\infty

y

approaches

- \infty

; as

x

approaches

- \infty

y

approaches

\infty

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Verified step by step guidance

Step 1: Identify the degree of the polynomial. The degree is determined by the highest power of x in the polynomial. In this case, the highest power is x^9, so the degree of the polynomial is 9.

Step 2: Determine the leading term of the polynomial. The leading term is the term with the highest power of x, which is 10x^9. This term dominates the behavior of the polynomial for large values of x.

Step 3: Analyze the coefficient of the leading term. The coefficient of 10x^9 is positive (10). A positive coefficient for an odd-degree polynomial indicates that as x approaches infinity, y approaches infinity, and as x approaches negative infinity, y approaches negative infinity.

Step 4: Consider the end behavior of the graph based on the leading term. For odd-degree polynomials with a positive leading coefficient, the graph rises to infinity on the right side (as x approaches infinity) and falls to negative infinity on the left side (as x approaches negative infinity).

Step 5: Conclude the end behavior of the polynomial function. As x approaches infinity, y approaches infinity; as x approaches negative infinity, y approaches negative infinity.