I'm kinda stuck on some of these calc concepts dealing with transcendental function, so if anyone could help me understand this I'd greatly appreciate it.
The question reads:
A rectangle has vertices A(x,lnx) B(x,0) C(3,0) and D(3,lnx) where 1
1) Find an expression that gives the area of the rectangle as a function of x
2) The area of this rectangle is maximized for some value "r" between 1 and 3. Write the expression that would solve for "r". You don't actually have to find "r"
The question reads:
A rectangle has vertices A(x,lnx) B(x,0) C(3,0) and D(3,lnx) where 1
2) The area of this rectangle is maximized for some value "r" between 1 and 3. Write the expression that would solve for "r". You don't actually have to find "r"
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1) The width of the rectangle is ln x, and the length, 3 - x.
Area = (3 - x) ln x = A(x)
2) To maximize the area, A'(x) = (3 - x) • 1/x + ln x • (-1) = 0
3/x - 1 - ln x = 0
x ≈ 1.8545507... ≈ 1.855 = r (Oops! I solved for r.)
Area = (3 - x) ln x = A(x)
2) To maximize the area, A'(x) = (3 - x) • 1/x + ln x • (-1) = 0
3/x - 1 - ln x = 0
x ≈ 1.8545507... ≈ 1.855 = r (Oops! I solved for r.)