optimization homework

[edgy shuttle]

I just literally don’t know what to do, and my professor explained it very badly, I just need the answer to these last  two questions so the assignment is not late and I can get help next week 

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[delicate pecan]

so you can express the boating distance using pythag as sqrt(4^2 + x^2), and the walking distance as 14-x. Using t=d/r you can express boating time as sqrt(4^2 + x^2)/2.8, and walking time as (14-x)/5. what you want is for the time to be at a minimum, so you can diff the sum of it [sqrt(4^2 + x^2)/2.8 + (14-x)/5] with respect to x to find dt/dx, which is the rate at which the time changes with respect to x, and then set it equal to zero and u should find a minimum point

then solve for x

so diff this and set to zero, then solve for x is the gist

wait actually no, theres a faster way

consider the point P(a, a^2)

you set up an equation giving the distance from P to (6, 1/2)

so this

then you diff it and set that equal to zero then solve for a, then plug that a value back in to this equation above