Finding Critical Numbers
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- เผยแพร่เมื่อ 29 ก.ย. 2024
- This calculus video tutorial explains how to find the critical numbers of a function. These include trig functions, absolute value functions, rational functions, fractions, square roots and more. To find the critical number, find the first derivative of the function, set it equal to zero, and solve for x. If you have a fraction as a derivative, set the numerator and denominator of the fraction equal to zero and solve. Critical numbers occur when f'(c) = 0 or when f'(c) does not exist as in the case of a cusp. This calculus video contains plenty of examples and practice problems.
Introduction to Limits:
• Calculus 1 - Introduct...
Derivatives - Fast Review:
• Calculus 1 - Derivatives
Introduction to Related Rates:
• Introduction to Relate...
_____________________________
Extreme Value Theorem:
• Extreme Value Theorem
Finding Critical Numbers:
• Finding Critical Numbers
Local Maximum & Minimum:
• Finding Local Maximum ...
Absolute Extrema:
• Finding Absolute Maxim...
Rolle's Theorem:
• Rolle's Theorem
________________________________
Mean Value Theorem:
• Mean Value Theorem
Increasing and Decreasing Functions:
• Increasing and Decreas...
First Derivative Test:
• First Derivative Test
Concavity & Inflection Points:
• Concavity, Inflection ...
Second Derivative Test:
• Second Derivative Test
_________________________________
L'Hopital's Rule:
• L'hopital's rule
Curve Sketching With Derivatives:
• Curve Sketching - Grap...
Newton's Method:
• Newton's Method
Optimization Problems:
• Optimization Problems ...
_______________________________________
Final Exams and Video Playlists:
www.video-tuto...
Full-Length Videos and Worksheets:
/ collections
Next Video: th-cam.com/video/WCq3sRzsJfs/w-d-xo.html
Final Exams and Video Playlists: www.video-tutor.net/
How did u get 0=x+1
You are the only thing keeping me from failing my calc class
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2:04 "set the numerator equal to x" - don't you mean equal to 0?
He did to zeeo that's how he got -4
in 15:14, why does the 9-x stay? Wouldn't it be just 1 since you are pulling out the (9-x)^1/2
that was what i was thinking as well, did you figure out why
Another interesting way to solve the absolute value problem is to realize that |x| = sqrt(x^2), and finding the derivative that way. Derivative of |x| would be |x|/x, then just use the chain rule. I thought that was an interesting alternate solution.
So whenever you are finding the critical number of a fraction/ rational function you set both the numerator and denominator equal to zero?
Yeah
Thank you so much for this video!! You helped me completing one of my homework questions and better understand how to find a critical number of a function.
I've taken calc 1 twice now, I did it in high school and now in college, both times I've used this channel to help study for the tests
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i wish you have covered the trig functions with a coefficient. trying to find zeros of sin(3x) for 0 less than x less than pi..... the anser is pi/6 and 5pi/6 but i dont see how... little help anyone??
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Can someone explain at 5:19 why we ignored 6?
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This video is wayyyyy better than the one on Khan Academy
at 19:40 isnt 1/2 divided by -1/2 gonna be -1? Why is it (9-X)^1
14:40
You’re dividing the exponents. So it’s like 1/2 - (-1/2)= 1/2 + 1/2= 2/2= 1
Why wen the derivative happens to be a fraction why do we have to equate them to zero separately??
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You helped me earn a 100 on my differential calculus exam
17:22 i think root of 9-x^2 had been smaller than 0, the interval would been critical. Am i right? Should we have considered this situation?
yes
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thank you for helping me find the crit
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but what happened to the 6 that was factored? 5:15
Don't know if this comment will help now but, he discarded the 6 because he wanted to find out what the x's have to be to make the number in the parentheses become zero. If one number in one of the parentheses becomes zero then the whole equation will become zero because zero times what ever number will automatically become zero.
The 6 is a constant and you can divide it by 0 and it disappears
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I was hooked when he didnt redraw the first graph 5 times to get the perfect smoothness. I hate when math teachers do that.
Professor Organic Chemistry Tutor, thank you for an exceptional video/lecture on Finding Critical Numbers in Calculus One. Finding Critical Numbers is important in all levels of Advanced Mathematics. This is an error free video/lecture on TH-cam TV with the Organic Chemistry Tutor.
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17:19 Nice
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At 2:05, what do you mean by, "if we set the numerator equal to x"? Did you mean "set the numerator equal to -4"? I'm confused
If he solves the top of the equation as in 2x+8=0 and solves for x it'll be -4, at least that's what I'm guessing lol
17:20 .......nice
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many examples help A TON
A vertical asymptote counts as a critical points?
saved me from despair.
Can someone explain please how setting it to zero equals it to -1 @ 3:20
You subtract both sides of the above equation i.e 0=x+1 by -1. Thus, 0-1=x+1-1. The 1s cancel each other out leaving behind: -1 = x or x=-1.
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Thank you for the explanation by the way.
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Whats the difference of critical point and critical number
Let us assume critical number is c. Critical point is ( c, f(c))
why cant x = 0 when sinx = 0
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Still not watched full 😭
Φουερ Μάθ ψήφ μετεω διδ 2
once again thank you so much for the help !!!!
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Whats the difference of critical point and critical number
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19:00 why are we dividing -sinx when there’s a sum(or substraction) there?
That's called "factoring".
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Life saver! Can you help me out with this equation- find the critical points for 9e^x-e^3x+6
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Sir why we compare the 1st derivative with 0
Because it's the only way to find the critical number/numbers
Because when the derivative is 0 there is a horizontal tangent line where the slope is 0.
is "e" a local maximum
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Finally I get it! Thank you!
Thanks man
Great explanation JG, as usual.
On example 2. If you factor by the quadratic formula, you get x = -2 ; x = -3. Unless I simply just made a simply math error. I believe the critical numbers are -2,-3. Please correct me if I am wrong.
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