Verify that the Intermediate Value Theorem applies to the indicated interval and find the value of c guaranteed by the theorem.
1 answer:
If you plug x = 5/2 = 2.5 into f(x), you'll get 5.83 approximately as the output. If you plug in x = 4 into f(x), then you'll get 6.67 as your output. The question is this: "Is the value 6 in that output interval from 5.83 to 6.67?". The answer is "yes, the value of 6 is between those two mentioned values". So the intermediate value theorem does apply here. How do we find that value of c? We simply replace f(x) with 6 and isolate x. See the attached image for the steps on how to do that. The final result of that attached image below is x = 2 or x = 3, but I'm able to rule out x = 2 as its not in the interval [2.5, 4]. The only thing left is x = 3
Final Answer: 3
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Let's say the numbers are "a" and "b"
hmm say "a" is the smaller, and "b" the greater
so "b" is "4 more than 5 times" "a"
so... 5 times "a" is 5*a or 5a
4 more than "that", will be "that" + 4
or
5a + 4
so.. whatever "a" is, "b" is 5a+4
now, their sum is 22, as opposed to "zz" hehe
so
solve for "a", to see what the smaller one is
what's "b"? well, b = 5a + 4
hmm say "a" is the smaller, and "b" the greater
so "b" is "4 more than 5 times" "a"
so... 5 times "a" is 5*a or 5a
4 more than "that", will be "that" + 4
or
5a + 4
so.. whatever "a" is, "b" is 5a+4
now, their sum is 22, as opposed to "zz" hehe
so
solve for "a", to see what the smaller one is
what's "b"? well, b = 5a + 4