Michael L. answered • 12/04/23
Tutor
5.0
(224)
25 years experience, including AP and college Calc 1-3
The video goes over how to visualize and set up the problem and get the equation to optimize. If you need further help with the First Derivative Test to actually perform the optimization, let me know.
Michael L.
tutor
Yikes! You're right, I don't hear sound either. I'll try and find out what went wrong and, if necessary, re-record. (Funny, my equipment had been working fine...)
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12/04/23
Michael L.
tutor
I can't find any way to delete and re-record the video. Mark M., thanks for pointing out the lack of sound (so weird, a video I recorded just minutes before did have sound). Soyeb, if you're reading this, here's a written explanation of what I did in the video: you'll see a little right triangle inside a big right triangle. The height of the little one is 3, the height of the fence, and the base is x, the unknown distance from ladder to fence. The height of the big one I called h and the base is 3+x, distance from fence to building plus unknown distance to foot of ladder. The hypotenuse is L, the length we want to minimize. Use the Pythagorean Theorem to write that length as Sqrt( (x+3)^2 + h^2 ). You can't minimize that because there are 2 variables. But the little triangle is similar to the big triangle so h/3 = (x+3)/x. Solve for h, plug into the square root formula. Now you have a formula with only x:
Sqrt ( (x+3)^2 + 9(x+3)^2/x^2 ). You can use the First Derivative Test to find the critical value and the minimum. Suggestion: square the function before taking the derivative. You'll get the same value of x but with less work. And remember to plug x into the original function to get the length of the ladder.
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12/04/23
Mark M.
Are you sure this video has sound? I heard the opening music, but not the narration. Thanks.12/04/23