Question

What is the value of g'(0) if y=g(x) has a graph given by

Answer 1

Answer:

B. -4

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Algebra I

• Reading a coordinate plane
• Coordinates (x, y)
• Slope Formula: $\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}$
• Functions
• Function Notation

Calculus

Derivatives

• The definition of a derivative is the slope of the tangent line.

Step-by-step explanation:

Step 1: Define

Identify

We are given function y = g(x) in a graph.

Step 2: Find

In order to find the derivative g'(x) at x = 0, we must find the tangent line to x = 0.

We see from the graph that we can find/approximate the tangent line from points (1, -4) and (-1, 4):

1. Substitute in points [Slope Formula]:                                                              $\displaystyle m = \frac{4 - -4}{-1 - 1}$
2. [Fraction] Subtract:                                                                                           $\displaystyle m = \frac{8}{-2}$
3. Divide:                                                                                                               $\displaystyle m = -4$

∴ our answer is B.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Derivatives

Book: College Calculus 10e