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Expert-verified Found in: Page 249 ### Calculus

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861 # Last night at 6 p.m., Linda got up from her blue easy chair. She did not return to her easy chair until she sat down again at 8 p.m. Let s(t) be the distance between Linda and her easy chair t minutes after 6 p.m. last night.(a) Sketch a possible graph of s(t), and describe what Linda did between 6 p.m. and 8 p.m. according to your graph. (Questions to think about: Will Linda necessarily move in a continuous and differentiable way? What are good ranges for t and s?(b) Use Rolle’s Theorem to show that at some point between 6 p.m. and 8 p.m., Linda’s velocity v(t) with respect to the easy chair was zero. Find such a place on the graph of s(t).

(a) The graph of s(t) is,

(b) The graph for the tangent line is, See the step by step solution

## Part (a). Step 1. Given Information.

s(t) is the distance between Linda and her chair t minutes after 6 p.m.

## Part (a). Step 2. The graph of s(t)

The graph is, ## Part (b). Step 1. Given Information.

s(t) is the distance between Linda and her chair t minutes after 6 p.m.

## Part (b). Step 2. The Rolle's Theorem.

Rolle's Theorem states that if$f$ is continuous on $\left[a,b\right]$ and differentiable on $\left(a,b\right)$, and if $f\left(a\right)=f\left(b\right)=0$, then there exits atleast one value $c\in \left(a,b\right)$ for which $f\text{'}\left(c\right)=0$.

The tangent line to the graph at $x=c$ be a horizontal line.

The graph showing the tangent line is,  ### Want to see more solutions like these? 