The function P(x) = - 2.75x^2 + 1750x

The function P(x) = - 2.75x^2 + 1750x - 7000 gives the profit when x units of a certain product are sold. Find a) the profit when 75 units are sold dollars b) the average profit per unit when 75 units are sold dollars per unit c) the rate that profit is changing when exactly 75 units are sold dollars per unit d) the rate that profit changes on average when the number of units sold rises from 75 to 150. dollars per unit e) The number of units sold when profit stops increasing and starts decreasing. (Round to the nearest whole number if necessary.) units

Transcript

00:01 Hello everyone, in this problem we are given with the function p of x which is to be equal to minus 2 .75 x square plus 1750 x minus 7000 where p of x is the profit when x units are sold.

00:17 In the first part of the equation we need to find profit when 75 units are sold.

00:23 So we need to find p of x when x equal to 75.

00:27 So p of 75 will be substituting the value of x as 75 in the given function so it will be minus 2 .75 of 75 the whole square plus 1750 of 75 minus 7000.

00:42 So simplifying this we get this value to be equal to 108781 .25.

00:49 So therefore when 75 units are sold the profit is 108781 .25 dollars.

01:09 Now let us move on to the next part of the equation where we need to find the average profit per unit when 75 units are sold.

01:16 So average profit per unit is given by the formula profit divided by number of units.

01:35 So substituting its here so the profit we obtained above is 108781 .25 divided by 75.

01:44 So simplifying this we get this value to be 1450 .416.

01:51 So therefore the average profit when 75 units are sold is 1450 .416 dollars.

02:15 In the next part of the equation we need to find the rate that profit is changing when exactly 75 units are sold.

02:22 So here we know that the profit function is given as minus 2 .75 x square plus 1750 x minus 7000.

02:33 Now differentiating with respect to x we get dp by dx to be equal to minus 5 .5 x plus 1750.

02:44 So now we need to find dp by dx when x equal to 75.

02:54 So dp by dx when x equal to 75 substituting the value of x as 75 over here so 5 .5 of 75 plus 1750.

03:05 So simplifying this we get this value as 1337 .5.

03:11 So therefore it is of dollars.

03:17 Therefore the rate that profit is changing when exactly 75 units are sold is 1337 .5 dollars per unit...

Question

Please give Ace some feedback