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Horizontal Tangent line. Determine the points (if any) at which the function has a horizontal tangent line.

Horizontal Tangent line. Determine the points (if any) at which the function has a horizontal tangent line.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Horizontal Tangent line. Determine the points (if any) at which the function has a horizontal tangent line.

The image shows a mathematical equation labeled with the number 60. The equation is a quadratic function expressed as: \( y = x^2 + 9 \) In this equation, \( y \) represents the dependent variable, and \( x \) represents the independent variable. The graph of this equation is a parabola that opens upwards with the vertex at the point (0, 9). This is because the equation is in the form \( y = x^2 + c \), where the coefficient of \( x^2 \) is positive. The term \( +9 \) indicates that the entire parabola is shifted 9 units upward on the Cartesian plane. The axis of symmetry for this parabola is the vertical line \( x = 0 \).
Transcribed Image Text:The image shows a mathematical equation labeled with the number 60. The equation is a quadratic function expressed as: \( y = x^2 + 9 \) In this equation, \( y \) represents the dependent variable, and \( x \) represents the independent variable. The graph of this equation is a parabola that opens upwards with the vertex at the point (0, 9). This is because the equation is in the form \( y = x^2 + c \), where the coefficient of \( x^2 \) is positive. The term \( +9 \) indicates that the entire parabola is shifted 9 units upward on the Cartesian plane. The axis of symmetry for this parabola is the vertical line \( x = 0 \).
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