SOLUTION: Find the maximum verical distance between f(x)=x^2 and the line y=6x-5 on the domain [1,5]

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Question 1012190: Find the maximum verical distance between f(x)=x^2 and the line y=6x-5 on the domain [1,5]
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Sketch first might help.
graph%28300%2C300%2C-2%2C8%2C-2%2C12%2Cx%5E2%2C6x-5%29
graph%28300%2C300%2C-2%2C8%2C-2%2C20%2Cx%5E2%2C6x-5%29

Look at h%28x%29=%286x-5%29-x%5E2.
dh%2Fdx=d%286x-5-x%5E2%29%2Fdx
dh%2Fdx=6x-2x

Expect maximum when 6x-2x=0.
x%286-2x%29=0
2x%283-x%29=0
and graph sketched suggests a MAXimum difference will be at 3-x=0, or highlight%28x=3%29. Also, question specified the interval on x between 1 and 5.