How to Optimize the Viewing Angle Using Calculus | Math Application

[@Alceste_]

Interesting how close yet different the intuitive answer of 50ft is from the analytic result.

[@learnmathbydoing]

That's a great observation!

[@diatribeeverything]

Just discovered your channel. Great stuff! Keep it up. Subbbed.

[@learnmathbydoing]

Awesome, thank you!

[@unebonnevie]

Nice. Two application points mentioned in the vid. 1) To maximize something, take the 1st derivative. 2) The critical point of the derivative (equation) is zero to find the maximum value of the interested variable, the angle theta in this case.

[@5729ariel]

Great video!

[@learnmathbydoing]

Thanks!

[@vinodvenkatesan]

What tool do you use for your animations? Thanks

[@learnmathbydoing]

Just PowerPoint. The secret to create movement is the morph transition. Create (duplicate) two slides, and create some changes in the second slide. When you run those two slides with morph transitions, any changes from the first slide to the second slide will appear a motion, so with that as the idea, you can create the animation you want fairly easily. Here is how I usually do the animation. How to Animate Math Equations #math kzbin.info/www/bejne/iZCoqmN3gMmtnK8

[@vinodvenkatesan]

@learnmathbydoing Thank you for the detailed explanation.

[@mnek742]

Nice problem! One can also use theta = tan^-1(x/45)-tan^-1(x/55)

[@DanChereches-e8q]

Nice idea for a problem However that calculation looks unnecessary to me. If T=55/x and B=45/x the tangents of top and bottom angles then by angle difference formula for tangent tan(theta)=Tan(top_angle-bot_angle)=(T-B)/(1+TB)=10x/(x^2+9*11*25) that is 55 or 45 but i just factored it out this thing is much nicer to differentiate and knowing the functions is uniformly increasing the min/max will not be changed. tan'(theta)=(10*(x^2+9*11*25)-10x*2x)/(x^2+9*11*25)^2=(10*45*55-10x^2)/(x^2+9*11*25)^2 so we got the extrema points of x=+-15sqrt(11) I don't think the difference is major but i just didn't feel like working with the arctangent lol

[@michetix7885]

Well that small guy could solve it by walking

[@cradleofrelaxation6473]

And I calculate this critical angle in my head when watching live performance. Ama phoking genius!!