SOLUTION: Could you please help me with this Calculus problem? My understanding is that I need to use the Intermediate value theorem to solve this but am not sure.
Would greatly apprecia
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Would greatly apprecia
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Question 1203493: Could you please help me with this Calculus problem? My understanding is that I need to use the Intermediate value theorem to solve this but am not sure.
Would greatly appreciate your help.
Found 2 solutions by ikleyn, math_tutor2020:Answer by ikleyn(52851) (Show Source):
You can put this solution on YOUR website! .
Could you please help me with this Calculus problem? My understanding is that I need to use the Intermediate value theorem to solve this but am not sure.
Would greatly appreciate your help.
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The answers and the solutions by @math_tutor2020 for (a) and (b) are INCORRECT.
The correct answers for (a) and (b) are " ALWAYS TRUE ".
(a) Assume for a minute that there is no such "c" in the interval [-3,9] that g(c) =/= 49.5.
Then it means that g(x) is identically equal to 49.5, but it CONTRADICTS to the given information.
The contradiction proves that statement (a) is ALWAYS CORRECT.
(b) The reasoning for (b) is PRECISELY the same. Statement (b) is ALWAYS CORRECT.
(c) Statement (c) is the direct consequence of the Intermediate value theorem.
Statement (c) is ALWAYS CORRECT.
I will stop at this point, since I do not like to solve many problems in one post.
I also do not believe that solving many problems / (answering many questions)
in one post is a good educational strategy.
In opposite, it is a way to create a mess.
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Some time later today I read other solutions/answers by @math_tutor2020 and was horrified.
His answers (d) and (e) are also FATALLY INCORRECT.
The correct answers for (d) and (e) are
- (d) NEVER TRUE;
- (e) ALWAYS TRUE.
These my answers for (d) and (e) are OBVIOUS, or, as I sometime says, MORE THAN OBVIOUS.
(