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A manufacturer finds that the revenue generated by selling x units of a certain commodity is given by the function R(x) = 60x − 0.5×2, where the revenue R(x) is measured in dollars. What is the maximum revenue, and how many units should be manufactured to obtain this maximum?

Find the inverse function of f. f(x) = 7×3 + 4

Weather balloons are filled with hydrogen and released at various sites to measure and transmit data about conditions such as air pressure and temperature. A weather balloon is filled with hydrogen at the rate of 0.5 ft3/s. Initially, the balloon has 2 ft3 of hydrogen. (a) Find a linear function V that models the volume of hydrogen in the balloon at any time t. (b) If the balloon has a capacity of 18 ft3, how long does it take to completely fill the balloon?

(a) Describe the end behavior of the polynomial.  y = x3 − 3×2 + 4x − 15 (b) Use the Factor Theorem to show if x − 3 is a factor of P(x). P(x) = x4 + 4×3 − 19×2 − 36x + 90

Consider the following functions. f(x) = 4x + 7,    g(x) = 3x − 1 Find  (a) (f ∘ g)(x) (b) (g ∘ f)(x)

Draw the rough graph of the following functions (a)  (b)

(a) Find the domain and range of the function (b) Sketch the graph of 

What is one aspect of management that has surprised you so far in this course?

When firms try to meet the same needs/demands as their competitors, it leads to… Imitation Excessive focus on operational effectiveness Zero-sum competition (one firm’s gain in market share is another’s loss)

The best theatre shape is: