This makes sense if you’re looking at how the tangents change from left to right on the curves. If you look at the tangents from right to left it breaks down. On the concave down shape, from right to left, the tangent is decreasing to 0 then getting steeper but in a positive way.

Bless Khan Academy during corona virus pandemic 🙏🙏🙏

thank you very Much, so helpful

Actually, there are TWO cases where the Second Derivative Test is inconclusive: (1) f"(c) = 0 (you have that one), and (2) f"(c) undefined (you missed that one). It IS possible for f'(c) to be DEFINED but f"(c) to be UNDEFINED. For example, consider the function f(x) = x^(4/3). Then f'(x) is essentially x^(1/3) which is 0 only for x = 0, so x = 0 is a critical number (the only one, since f'(x) is never undefined). Then, f"(x) is essentially x^(-2/3), which is UNDEFINED for x = 0, so the Second Derivative Test is INCONCLUSIVE for the only critical number for f, x = 0. However, if we use the First Derivative Test, we find that f'(x) is negative for x to the left of 0 and positive for x to the right of 0, so clearly (0,0) is a local MINIMUM point.

Sir, thanks for _existing_

Why is 2nd derivative of functions -ve for max and +ve for min

using of different colors is awesome!

@jaredmorales9763

4 жыл бұрын

Umair facts it looks really nice

@jaredmorales9763

4 жыл бұрын

Lowkey makes you more interested and makes it less monotonous

What is the higher operation needed to determine the concavity of a function with a critical point of 0?

@hippzhipos2385

6 жыл бұрын

Noone knows answer

How u set pen for writing

do sal do this with a mouse?

@kingstarsky9739

6 жыл бұрын

no...

this might be obvious but how did you get -4 for the second derivative?

@notatruestatement

7 жыл бұрын

It's a hypothetical.

@HassHansson

5 жыл бұрын

its just an example

wait. Isn't the second diff of a quadratic a point?

@jimmybob609

4 жыл бұрын

Let’s for example use x^2 f’x=2x so the rate of change of our function is 2x. The second derivative would be 2, which would be the rate of change of our first derivative which is constantly changing by a factor of 2.

@nohackers2037

4 жыл бұрын

@@jimmybob609 yes. Your comment helped out a lot dy/dx is y/x also known as rate Example d/t = S (distance travelled per unit time) is rate. Also gives you a slope at any given point (d/t)/t = second derivative which tells you what happens as the rate changes over time eg: speed/t = acceleration. is the change of speed

@nohackers2037

4 жыл бұрын

@@jimmybob609 wait. clarify this for me the second derivative determins how pointy is a function for x^3? and x^2 right?