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Len [333]
3 years ago
13

9. Let f be a continuous function such that f(3) = 4 and f(5)=2. Let h(x)= f(x) + 2x. Explain why

Mathematics
1 answer:
GaryK [48]3 years ago
4 0

Since <em>f(x)</em> is continuous, so is <em>h(x)</em>.

Also, since <em>f</em> (3) = 4 and <em>f</em> (5) = 2, we have

<em>h</em> (3) = <em>f</em> (3) + 2•3 = 4 + 6 = 10

<em>h</em> (5) = <em>f</em> (5) + 2•5 = 2 + 10 = 12

It follows from the intermediate value theorem that there is some <em>t</em> between 3 and 5 such that <em>h(t)</em> is between 10 and 12, and namely there is some <em>t</em> for which <em>h(t)</em> = 11.

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