Sketching Derivatives From Parent Functions - f f' f'' Graphs - f(x), Calculus

This calculus video tutorial explains how to sketch the derivatives of the parent function using the graph f(x). This video contains plenty of examples and practice problems.
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Here is a list of topics:
1. Sketching Derivatives of Parent Functions
2. Quadratic Function / Parabola f(x) = x^2
3. Linear Functions 2x
4. Cubic Functions x^3
5. Trigonometric Functions - Sine and Cosine - sin(x) and cos(x)
6. Increasing and Decreasing Functions
7. Relative Extrema of a Function and the Derivative f'
8. Graphing The First and Second Derivative of a Function
9. Local Maximum and Minimum Calculus
10. Critical Points and Inflection Points
11. Relative Maximum and Minimium of Using the First Derivative Graph
12. Critical Points and Extrema - Calculus
13. Concavity, Inflection Points on Graph of f'(x) - First Derivative
14. Identifying the Horizontal Tangent Lines
Disclaimer: Some of the links associated with this video may generate affiliate commissions on my behalf. As an amazon associate, I earn from qualifying purchases that you may make through such affiliate links.

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Error: At 23:18, you list the Concave Down point as (-1,1) when it should be (-1,2)

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Graph 8. CD on (-4,-3) U (-1,2)

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Put different values of x in the equation {Say, for example, f(x)=x^2}, note down the corresponding values for f(x). Mark these values of x and their corresponding values for f(x) on the co-ordinate axis. P.S: Take f(x) as your vertical axis and x as the horizontal axis.

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How would you graph the derivative of a function with a hole at a point?

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What does it mean to change instantaneously at 12:23??

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how to find from which side it goes up or down? for example fx= x^2

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from this can we find absolute min and max point?

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5:50 how is that increasing the arrows going down?

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The slope of f becomes the y value of f prime

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at 24:45 shouldn't the function be increasing at -2 to -1 and 2 to 3 alsoh because first derivative is also positive there .please answer iam really having trouble understanding this area . thanks

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23:09 isn’t the second concave down interval from -1 to 2? Like this (-1,2)

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C up at 22:29 is (-2 to infinity)

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Conc Down : (-4,-3) U (-1, 1) I thought the 2nd one would be (-1, 2). Please someone clarify. Thanks!

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yes the second interval where the function concave down supposed to be (-1,2), because the second derivative on the interval (-1,2) is negative (meaning the rate of the first derivative function on interval (-1,2) is decreasing). I think he just did a typo.. CMIIW

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Did the f=X^2 for the original function come out of thin air?

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F increasing decreasing fprime negative positive

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Increasing - positive, zero, decreasing - negative.

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22:48 concave down - wasn't it supposed to be (-4,-3)u(-1,2) .. and not (-4,-3)u(-1,1)

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Can someone tell me how to plot graph of f' when graph of f is given but not the value of f

[@staycalm9979]

That is exactly what he teaches us at 7th minute in this video. Notice that there is no value given for the f(x) but still he manages to plot f'(x). Important point here is, slope of the original function f(x) is the Y-value for the derivative function. It doesn't have to be an exact graph like on computer. It is just an approximate graph. Examiners will not expect you to draw an exact graph. Imprint that point in your mind.

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23:15 why is it concave down from (-1 to 1) and not (-1 to 2)

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He just made a mistake. It should be what you said it should be