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Q. 62

Expert-verifiedFound in: Page 249

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,

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

The graph is,

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

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

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