consider the cost fucntion c(x)=6x^2+14x+18?

// You haven't provided information about the cost function c(x); I'm assuming it

// denotes x as the number of units and the cost is in thousands of dollars ?

// It has to have the same units as the revenue function.

c(x) = 6x² + 14x + 18

r(x) = -x² + 37x + 38

// The breakeven point occurs where the two functions intersect, in other words,

// where c(x) = r(x)

c(x) = r(x) ⇒

6x² + 14x + 18 = -x² + 37x + 38

7x² - 23x - 20 = 0

// Factor and solve for x

(7x + 5)(x - 4) = 0

x = -5/2 or 4

// we can ignore the solution x = -5/2 because it doesn't make sense to have

// negative #units

When x = 4

.....c(4) = 6(4)² + 14(4) + 18 = 170

.....r(r) = -4² + 37(4) + 38 = 170

So your break even point is at x=4, and y = 170.........ANS

(see below)

c) did you get x = 4....d) mc = 46 & mr = 28