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The function g I エ+5 15 6) is graphed. Determine which of the following statements is true about the function g The range of the function g is [-3. 5, 0]. From-7

The function g I エ+5 15 6) is graphed. Determine which of the following statements is true about the function g The range of the function g is [-3. 5, 0]. From-7

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Determine which of the following Statement is true about the function g
The image displays a graph of a mathematical function plotted on a Cartesian coordinate system. The x-axis ranges from -10 to 5, and the y-axis ranges from -5 to 15. The function appears to be a curve that crosses the x-axis at approximately x = -8 and x = 0, indicating two roots of the equation. The graph starts at a high point on the y-axis above 15 when x is less than -10 and decreases steeply, reaching a minimum around x = -9. It then rises back above the x-axis and peaks near y = 5 before descending again. The curve represents a non-linear polynomial function with at least one local maximum and one local minimum. There is a prominent red dot at the maximum point on the curve, around (-10, 15), likely marking a significant point of interest in the context of the graph's study, such as a local maximum or endpoint. This graph could be part of a lesson on polynomial functions, exploring concepts like roots, local extrema, and the general behavior of polynomial graphs.
Transcribed Image Text:The image displays a graph of a mathematical function plotted on a Cartesian coordinate system. The x-axis ranges from -10 to 5, and the y-axis ranges from -5 to 15. The function appears to be a curve that crosses the x-axis at approximately x = -8 and x = 0, indicating two roots of the equation. The graph starts at a high point on the y-axis above 15 when x is less than -10 and decreases steeply, reaching a minimum around x = -9. It then rises back above the x-axis and peaks near y = 5 before descending again. The curve represents a non-linear polynomial function with at least one local maximum and one local minimum. There is a prominent red dot at the maximum point on the curve, around (-10, 15), likely marking a significant point of interest in the context of the graph's study, such as a local maximum or endpoint. This graph could be part of a lesson on polynomial functions, exploring concepts like roots, local extrema, and the general behavior of polynomial graphs.
The function \( g(x) = -\frac{1}{15}x(x+5)(x-6) \) is graphed. Determine which of the following statements is true about the function \( g \). - The range of the function \( g \) is \([-3.5, 0]\). - From \(-7 \leq x \leq 6\), the function \( g \) has two decreasing intervals. - The function \( g \) has two relative maximums on the interval \(-7 < x < 6\). - The function \( g \) has one solution when \( g(x) = 1 \) on the interval \(-7 < x \leq 6\).
Transcribed Image Text:The function \( g(x) = -\frac{1}{15}x(x+5)(x-6) \) is graphed. Determine which of the following statements is true about the function \( g \). - The range of the function \( g \) is \([-3.5, 0]\). - From \(-7 \leq x \leq 6\), the function \( g \) has two decreasing intervals. - The function \( g \) has two relative maximums on the interval \(-7 < x < 6\). - The function \( g \) has one solution when \( g(x) = 1 \) on the interval \(-7 < x \leq 6\).
Expert Solution
Step 1

Consider the given figure of the function gx=−115x+5x−6.

We have to check which of the given statement is true.

(1) We have to check whether the statement, "The range of the function g is -3.5,0." is true or false.

From the given figure

The range of the function g is -7,6.

Hence, the statement, "The range of the function g is -3.5,0." is false.

 

(2) We have to check whether the statement, "From -7≤x≤6, the function g has two decreasing intervals" is true or false.

From the given figure

The function g has two decreasing intervals -7,-91+13 and 91+13,6 

Hence, the statement, "From -7≤x≤6, the function g has two decreasing intervals" is true.

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