Intermediate Value Theorem Explained - To Find Zeros, Roots or C value - Calculus
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- เผยแพร่เมื่อ 6 ก.พ. 2025
- This calculus video tutorial explains how to use the intermediate value theorem to find the zeros or roots of a polynomial function and how to find the value of c that satisfies the intermediate value theorem on a continuous interval. This contains plenty of examples and practice problems for you to master the concept. It shows you how to factor trinomials with leading coefficient of 1 and when it's not 1 in order to find the value of c. It also explains the IVT theorem using graphs.
Derivative Applications - Free Formula Sheet:
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Introduction to Limits:
• Calculus 1 - Introduct...
How To Evaluate Limits from a Graph:
• How To Evaluate Limits...
Evaluating Limits by Factoring:
• Evaluating Limits By F...
Limits of Rational Functions:
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Limits of Radical Functions:
• How To Evaluate Limits...
Limits of Trigonometric Functions:
• Limits of Trigonometri...
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How To Find the Limit at Infinity:
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Infinite Limits + Vertical Asymptotes:
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Limits at Infinity with Radicals:
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Limits of Absolute Value Functions:
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Limits of Composite Functions:
• How To Find The Limit ...
The Squeeze Theorem:
• Squeeze Theorem
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Limits and Logarithms:
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Limits of Exponential Functions:
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Piecewise Functions - Limits:
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3 Step Continuity Test:
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Not only did I learn how to use the IVT, but I refreshed my skills on factoring at the end! Thank you
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MR. Organic Chemistry Tutor, thank you for introducing the Intermediate Value Theorem. The Intermediate Value Theorem is an important theorem in Calculus One. This theorem is used to find the zeroes of any polynomial on a continuous interval.
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at 10:24 what you could do instead, to decrease time and make it easier on your self, is that since you multiplied the constant by two, now you need to divide the roots you got by two. In the example in the video, the roots are 7 and -4 so divide them by two you got 3.5 and -2. thats what my teacher used to do.
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4:09
-4 + -3 = -7, not -1
I know it is a small mistake and it hard to keep track of all the notations but just thought I'd share
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Quick question, is that y value always zero in every case or there are exceptions?
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3:40
Why is 0 chosen to equal the equation?
If I try with other numbers in the domain of -6 and 8 and equal to the equation, the equation is changed
because it's asking whats the root. root means when y = 0
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To test the c value you can also plug it into the original equation. So
19 = 2(2)^2 + 3(2) + 5 => 19 = 19
Thank you for this video💯
For the first example, you said that c has to be = to 0 but then in the second example c is 19 and never passes through the x-axis. Is this because the first question specifies finding the "root" while the second question doesn't?
Yeah, that is the reason as to why. If it's not explicitly stated to be the root, oftentimes it will not be. It all depends on the context of the question.
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