Question
Asked Oct 21, 2019
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Find the absolute maximum and absolute minimum values of f on the given interval.
f(x) In(x2 5x 9), [-3, 1]
absolute minimum value
absolute maximum value
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Find the absolute maximum and absolute minimum values of f on the given interval. f(x) In(x2 5x 9), [-3, 1] absolute minimum value absolute maximum value

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Expert Answer

Step 1
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The given function is f(x)= ln (x2+5x+9) with the interval -3,1 Differentiate the function f(x)In(x2 +5x+9) with respect to x to find the critical point d f(x)= (In(x2 +5x+9)) d (x*+ 5х +9 1 = 1 .- 2x 5 x 5x+9 2x5 x25x9

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Step 2
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Equate the first derivative to zero. 2x5 -= 0 x5x9 2x 5 0 2x -5 5 2 5 Thus, the critical point is x - 2

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Step 3
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Check the behaviour of the curve as follows. Substitute x -3 in f(x)=In(x2 +5x +9) f(-3)In((-3)+5(-3)+10) In (9 -15 9) In(3) Substitute x -1 in f (x)= In(x2 +5x +9). fIn()+5(1)+9) -In (1+5+9) =In (15)

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Tagged in

Math

Calculus