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

B. -4

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Reading a coordinate planeCoordinates (x, y)Slope Formula: FunctionsFunction 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):

Substitute in points [Slope Formula]:                                                              [Fraction] Subtract:                                                                                           Divide:                                                                                                              

∴ our answer is B.

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

Unit: Derivatives

Book: College Calculus 10e