How to find the maximum curvature of y=e^x

Calculus tutorial on finding the maximum curvature of y=e^x.
Here's how to get the curvature formula: • A faster way to derive...
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#calculus #bprpcalculus #apcalculus #tutorial #math

[@user-fp5qd7fi6w]

Bro's life flashed before his eyes at

[@daniel_77.]

U had a existential crisis at

[@niom9446]

3:48

[@mikehood6745]

Made me smile at

[@cdkw2]

What about the oscillating trig function? They might be fun to get curvature of!

[@michaelz2270]

If you want to simplify the algebra... it suffices to find the minimum of κ^2, given by e^(2x)/(1 + e^(2x))^3. Letting u = e^(2x) you are minimizing u/(1 + u)^3 = 1/(1 + u)^3 - 1/(1 + u)^2. The derivative of this is -3/(1 + u)^4 + 2/(1 + u)^3, which equals zero when -3 + 2(1 + u) = 0 or u = 1/2. Then κ^2 = (1/2) / (1 + 1/2)^3 = (1/2)*(8/27) = 4/27, so that κ is the square root of this or 2/(3 sqrt(3)).

[@fzlagges5849]

I was able to solve it by using v=e^x in the original K, and it simplified both the derivative and the solving parting.

[@romanvolotov]

the reasoning at

[@ianfowler9340]

Try my differential equation which is a necessary condition. See previous video.

[@joe4582]

We did have a similar exercise in with we needed to find the smallest line form a point on a e Funktion and its solution of the tangensequtaion

[@MrKoteha]

I've tried doing it with other functions and it's interesting that for the natural logarithm the max curvature turns out to be the same as for e^x (Although with a minus if you don't take the absolute value)

[@tobybartels8426]

Whenever you're dividing by a power or a root, it's simpler to change that to a negative exponent and use the Product Rule, than to use the Quotient Rule.

[@DEYGAMEDU]

8:00

[@kingforgotten9090]

I might be wrong but I think when you were taking the derivative of the function k you did the derivatives of e to the powers wrong where they should be -2/3e^(-5/3) and 4/3e^(1/3) so you brought the powers down correctly for the power rule just didn't subtract 1 from the exponent.

[@tobybartels8426]

9:58

[@yassiryassir-rp4to]

what is y = lnx

[@vinuthomas7193]

When would k be used instead of y''? And why is that the formula for k?

[@joeythreeclubs]

Please do tan(x) next please, I couldn't figure it out.

[@yassiryassir-rp4to]

im like a VIP audience

[@yassiryassir-rp4to]

9 june 2024 ???