For a and b use the Average Rate of Change formula. (f(b)-f(a)/b-a)
a. In all cases, the smaller number = a and the larger number = b. In this problem, a=2 and
b=4
– Plug in a for x in the equation given P(2) = 2(2)^2 – 5(2) + 10 = 8
– Plug in b for x now in the equation given P(4) = 2(4)^2 – 5(4) + 10 = 22
– Now you have f(a) = 8 and f (b) = 22
– Now plug them into the Average Rate of Change Formula (22-8/4-2) = 7 (in Hundreds)
so 700
b. For this problem repeat the step to find f(b) since b is the only variable that changed
– P(3) = 2(3)^2 – 5(3) + 10 = 13
– Plug in your new f(b) into the Average Rate of Change formula with your previous f(a)
– (13-8/3-2) = 5 (in hundreds or 500) [b is now 3 instead of 4]
c. For this problem I just posted my work to show the steps instead of trying to confuse
you with words! J
The Second part of C the answer is d. “when 2 items are sold, the profit is increasing at
a rate of $300 per item” (scroll down and I apologize in advance for my 2nd grader
handwriting)
d. Repeat same steps as shown in C, but instead x=4 instead of 2
Therefore the marginal profit when x=4 is 1100