27.1 QUESTION 27 (JUNE 2017)
Given g(x) = ax3 + bx+c, a = 0, which has the following properties.
f'(x) > 0 if x <-3 or x > 3
f'(x) < 0 if -3 f'(-3) = f'(3) = 0
f(0) > 0
Use the above information to draw a sketch of g.
(4)

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204

the revenue of the fitness center, y, is the product of two factors: the number of members and the fee paid by each member. there are 320 members now, but number of members goes down by 10 for each $5 increase in fees, so if x is the number of $5 price increases then members is equal to (320 - 10x). since the fee is currently $45, and the fee increases by $5 for every price bump x, the fee is given by (45 + 5x). so, revenue y is given by y = (320 - 10x)(45 + 5x).

using pemdas, (order of operations) you'll see the answer is 24.