Question

Find where the function fx) - 34 - 16? - 1922 + 6 is increasing and where it is EXAMPLE 1 decreasing -2000 SOLUTION (x) = 12x2 - 48x? - 384x = 12x(x-2)(x+) -2000 -6000 To use the I/D Test, we have to know where x) > 0 and where f(x) < 0. This depends on the signs of the three factors of fx), namely, 12X, X- and X We divide the real line into intervals whose endpoints are the critical numbers (smallest). O and (largest) and arrange our work in a chart. A plus sign indicates that the given expression is positive, and a negative sign indicates that it is negative. The last column of the chart gives the conclusion based on the 1/D Test. For instance, F(x) < 0 for 0 < x <3, so fis Select on (0,8). (It would also be true to say that Fis decreasing on the closed interval (0,8).) Video Example 4 12xX8 FX) Interval X-4 -ACCO decreasing on (-2,-4) Select on (-40) decreasing on (0,0) -Select on (0.00) OCX + The graph of shown in the figure confirms the information in the chart.
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Answer 1

fca) 374_1673_1922+6 fla= 1223 - 48%-3848 12962_42-32) = 121(2-8217+4) sign This depends on the qualch of the three factors of fkas, namely 121, 1-8 and +4 on Critical numbers, -40mallet), 0, ollargut) fuko for o cal8 so fin decreary on (0,8) also f decreary on (-2,-4) f'so for 1-4,0) and 18,0), so fincreaus (-2,0) and (8,00) interval floo f decreaus increang - 4LICO decreany increasing a>8 122 7-8 x+4 ac-4 + It' ocx<8 + t t + + t