Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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Concept explainers

Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…
Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …
Question
Find the formula of f(x), a polynomial function of a last degree
The image contains a graph plotted on a Cartesian plane. ### Description of the Graph: - **Axes**: - The horizontal axis (x-axis) ranges approximately from -10 to 10. - The vertical axis (y-axis) ranges approximately from -10 to 10. - **Curve**: - The graph displays a blue curve, which appears to represent a cubic polynomial function due to its distinctive S-shape. - The curve decreases, crosses the x-axis at around x = -2, reaches a minimum, then increases and crosses the x-axis again at around x = 2. It continues rising sharply as x increases. - **Intercepts and Critical Points**: - The curve intersects the x-axis near x = -2 and x = 2, suggesting these are roots of the function. - There is a visible turning point, possibly a local minimum, near x = 0. - **Grid**: - The background features a dot grid, indicating increments of 1 unit on both axes, which helps in estimating the position of the curve more accurately. This graph may be used to discuss topics such as the behavior of polynomial functions, their roots, turning points, and general curve sketching.
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Transcribed Image Text:The image contains a graph plotted on a Cartesian plane. ### Description of the Graph: - **Axes**: - The horizontal axis (x-axis) ranges approximately from -10 to 10. - The vertical axis (y-axis) ranges approximately from -10 to 10. - **Curve**: - The graph displays a blue curve, which appears to represent a cubic polynomial function due to its distinctive S-shape. - The curve decreases, crosses the x-axis at around x = -2, reaches a minimum, then increases and crosses the x-axis again at around x = 2. It continues rising sharply as x increases. - **Intercepts and Critical Points**: - The curve intersects the x-axis near x = -2 and x = 2, suggesting these are roots of the function. - There is a visible turning point, possibly a local minimum, near x = 0. - **Grid**: - The background features a dot grid, indicating increments of 1 unit on both axes, which helps in estimating the position of the curve more accurately. This graph may be used to discuss topics such as the behavior of polynomial functions, their roots, turning points, and general curve sketching.
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To find the polynomial f(x) whose graph is given 

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