**Educational Content on Derivatives and Graph Analysis****Understanding Graphs: Position, Velocity, and Acceleration**The image presents three graphs representing a position function, \( s(t) \), a velocity function, \( v(t) \), and an acceleration function, \( a(t) \), each as a function of time, \( t \). You are required to estimate the \( x \) values to 1 decimal place.**Graph Descriptions**:- **Graph S**: Red curve- **Graph L**: Blue curve- **Graph D**: Dotted curve**Tasks and Questions**:(a) **Intervals where Graph L is increasing**: To determine these intervals, observe where the slope of Graph L is positive.(b) **Graph with decreasing slopes for \( x < 1 \)**: Identify the graph where the slope becomes less positive or more negative as \( x \) decreases below 1.(c) **Graph with always positive second derivative**: A positive second derivative indicates that the graph is concave up. Determine which graph maintains this property across its entire domain.(d) **Intervals where Graph S is concave down**: A graph is concave down when its second derivative is negative. Identify the segments of Graph S where this condition holds.(e) **Intervals where Graph S's second derivative is negative**: This is a similar analysis to part (d), focusing on the negativity of the second derivative specifically for Graph S.By carefully analyzing these graphs, one can leverage first and second derivatives to describe functional behaviors, such as intervals of increase/decrease, concavity, and extreme values.

0 -0.5 Graph S 0.5 Graph L 1 1 1 Graph-D D4 I can use the first and second derivatives to describe the behavior of functions, including listing intervals of increasing/decreasing, concavity, extreme values. (a) List the intervals where Graph L is increasing. (b) List a graph that has decreasing slopes when x is less than 1. 2.5 (c) Which graph has a second derivative that must be always positive? How do you know? (d) List the intervals where Graph S is concave down. (e) List the intervals where Graph S's second derivative is negative.

0 -0.5 Graph S 0.5 Graph L 1 1 1 Graph-D D4 I can use the first and second derivatives to describe the behavior of functions, including listing intervals of increasing/decreasing, concavity, extreme values. (a) List the intervals where Graph L is increasing. (b) List a graph that has decreasing slopes when x is less than 1. 2.5 (c) Which graph has a second derivative that must be always positive? How do you know? (d) List the intervals where Graph S is concave down. (e) List the intervals where Graph S's second derivative is negative.

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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Ex.4-6 This is my last question this month and I need the answer for these multiple choice No work needed just answers Thank you in advance for helping me
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the second derivative has a typo, it is -1 instead of 1 ?′′(?) < 0 ?? ? ∈ (−5,1) ∪ (2,6) The question is asking to sketch the graph with these provided information (SEE Image)
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