Screen Shot 2019-11-30 at 11.11.55 PM.png - 5 For the function f(x = 3x4 8x3-18x2 5 find a the critical numbers J x = 12X 3 24x = 36 X fi x = 0 12 x 3

Screen Shot 2019-11-30 at 11.11.55 PM.png - 5 For the...

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Unformatted text preview: 5. For the function f(x) = 3x4 +8x3 -18x2 +5, find a) the critical numbers; J' ( x ) = 12X 3+24x = 36 X fi( x ) = 0 12 x 3+ 24 X - 36 * = 0 12 x ( x 2+ 2 X - 3 )20 X = 0 , - 1, 3 b) the open intervals where the function is increasing; Increasing ( 0, 20 ) c) the open intervals where the function is decreasing. decreasing (-20, 01/ / The total profit P(x) (in thousands of dollars) from the sale of x units of a certain prescription drug is given by P(x) = In(-x3 + 3x2 +72x+1) for x in [0, 10]. a) Find the total number of units that should be sold in order to maximize the total profit. P' (X ) = * 3 + 3 *2+ 72x +1 ( - 3 x 2 + 6* + 72 ) 0 pi(x ) = 0 - -X3 + 3x 2 + 72x+1 ( - 3 x 2 +48 + 72 ) = 0 -- 3 x 2 +4x + 72 = 0 - 3 (x + 4 ) ( x - 6 ) = 0 - X = - 4 6' 24 x = 0 -# In(1 ) = 0 * = 6 -D In ( 325 )= 5.78383 5 # to b) What is the maximum profit? in thayanet ) = 10 - In ( 21 ) = 3. 04452/ (PCX ) = 5.78383 / Given f(x) = -2x3 -9x2 +108x-10, find the open intervals where the function is concave upward neave downward. Find any points of inflection. + to Concave upward (x ) = - 6x218 x+ 108 1- 3 00 ) < 2 - 18 x + 108 = 0 - 12x - 18 = 0 - 12x = 18 Concave downward 2 + 3x - 18) = 0 -12 - 12 X - 3 ) ( * +6 ) X = - 3 4 of 7 N/ M 5 POT =(- 3 - 371 f" ( - 5) =427 2 2...
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