Question

Question is below.

Answer 1

If it wasn't clear, I need help with part C.

Answer 2

A min/max value for a function occurs when its derivative equals 0

Answer 3

here,
In part a, you have an expression for the length of ladder function

Answer 4

In part b, you have its derivative

Answer 5

simply set the derivative equal to 0 and find the value of \(\theta\)

Answer 6

So using the derivative function equal to 0, I'd find the value of theta that could either yield the max or min value of the ladder's length?

Answer 7

Exactly

Answer 8

I attempt to proceed as follows but find that no solution can be calculated. Did I make another mistake? Thank you for helping by the way.

Answer 9

\(\sin^3 \theta = \cos^3\theta\)

can we conclude
\(\sin\theta = \cos \theta \implies \theta = \pi/4\)

because \(\theta\) is an acute angle ?

Answer 10

Plug that in the length expression for ladder in part a

Answer 11

That was a major brain block. Thank you so much!