Difference between revisions of "009A Sample Midterm 2, Problem 2"
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| − | <span class="exam"> | + | <span class="exam">The function <math>f(x)=3x^7-8x+2</math> is a polynomial and therefore continuous everywhere. |
| − | + | ::<span class="exam">a) State the Intermediate Value Theorem. | |
| − | ::<span class="exam">a) | + | ::<span class="exam">b) Use the Intermediate Value Theorem to show that <math>f(x)</math> has a zero in the interval <math>[0,1].</math> |
| − | ::<span class="exam">b) | ||
Revision as of 08:51, 5 February 2017
The function Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x)=3x^7-8x+2} is a polynomial and therefore continuous everywhere.
- a) State the Intermediate Value Theorem.
- b) Use the Intermediate Value Theorem to show that Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x)} has a zero in the interval Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle [0,1].}
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Solution:
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(b)
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| (a) |
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