A graphing Graph the function P in an appropriate viewing re

A graphing Graph the function P in an appropriate viewing rectangle and use the graph to answer the following questions answer to the integer that gives the company the least positive and sells only 10 blenders.) How many blenders must the firm produce to break even? (Round your

Solution

1) P(x)= 8x + 0.3x^2 - 0.0013x^3 - 373

Break even point is where P(x) = 0

8x + 0.3x^2 - 0.0013x^3 - 373 = 0
. . . x = 25.23 <== first break even point (moving positive as x increases)
. . . x = 250.76 <== second break even point (moving negative as x continues to increase)

P = 8x + 0.3x^2 - 0.0013x^3 - 373
P \' = -0.0039x^2 + 0.6x + 8
-0.0039x^2 + 0.6x + 8 = 0
. . . x = - 12.3 <== invalid negative production
. . . x = 166.2 <== production for maximum profit

2) t = [3*log(n/90)]/log2

t = [3*log(2000000/90)]/log2

t = [3*log22222.22]/log2 = 43.3 hrs

3) 3*log₇x + 3*log₇y – 4*log₇z

= log₇x³ + log₇y³ + log₇z^-4

= log₇(x³*y³*z^-4)

4) P(x) = x^4 – 4x^2 – 5

a) P(x) = 0 = x^4 – 4x^2 – 5

x = 2.24, -2.24, +I, -i

b) Factors = (x^2 +1)(x^2 - 5)