Suppose a baby food company has determined that its total revenue r for its food is given by r = − x ^3 + 102 x ^2 + 1575 x where r is measured in dollars and x is the number of units (in thousands) produced. what production level will yield a maximum revenue?

75 thousand

Step-by-step explanation:

R = -x³ + 102x² + 1575x

To maximize R, find dR/dx and set to 0:

dR/dx = -3x² + 204x + 1575

0 = -3x² + 204x + 1575

0 = x² − 68x − 525

0 = (x + 7) (x − 75)

x = -7 or 75

Since x can't be negative, x = 75.

Therefore, the revenue is a maximum when 75 thousand units are produced.

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation: