A company that manufactures travel clocks, has determined that the daily Marginal Coast function associated with producing T's clocks is derivative of C of X equals 0.9 times X square, minus 0.9 times X plus eight we're seeing Derivative of X is measure in dollars per unit, and X denotes the number of units produced. Management has also determined that the daily fixed coast incurring producing these clocks is $120. And with that information, we want to find the total cost incurred by the company in producing the first 500 trouble clocks per day. Right so way have the marginal cost function that is the derivative of the cost function. We want to find the glucose. So we got to find the until derivative or indefinite integral off. It's c prime. So we know that total cost see of X will be equal to the integral off the marginal coast. Uh huh. What? And that will be equal to the integral. The indefinite integral off the expression given to Thean marginal coast that is zero point 000 seriously or nine x square, then minus 0.9 x plus eight differential ipix. And we got to integrate this and this is a constant. So we get 0.9 times interval of X Square minus 0.9 which is a constant times the integral of X plus eight Internal of Differential of X And these are powers of acts and we know how to integrate that. It's 0.0 00 Sierra nine x to the third over three minus 0.9 times X squared over two plus eight eggs, plus a constant of integration. We put the continent's constant of integration at the end because even if each integral has a constant of integration, we know that some of them will be a unique constant of integration. So the tractor off being indefinite is the reason why we have constant of integration, which has to be determined with some initial condition. Let's simplify a little bit here, so we have 0.0 9/3 0 point 000003 X cube minus 0.9 Number two is 0.0 45 x square plus eight x plus c and this is the total cost function. With it, we can calculate it'll cost at any for any number of units. But before we get to determine this value, the value of this constant of integration. And for that we have the initial value given here. The management determined that daily fixed coast in current position disclose clocks is $120 the people. So because see of zero is 120 the fixed cost of position the unit, it's $120. I remember this function is given in dollars. It's important because the marginal coast is given in dollars per unit. So the coast, because it will be given in dollars so see of Siri's is 120. If we relate this expression at zero X equals zero, we get C. So so you gotta be 120. Okay, then The total cost function is 0.3 X cube minus 0.0 45 X square, plus a X plus 120 in dollars. And now we are able to calculate. What the problem is asking for is to find the total cost incurred by the company in producing the 1st 505 o'clock per day. So total cause mhm off producing to first. Okay, 500 clocks or traffic clock ace. See, at 500 that is 0.3 times 500 to the third, minus 0.0 45 500 square. Right. Plus eight times 500 plus 120. And using a calculator, find disease equal to 3000 370. So okay, during coast Uh huh. Incurred by the company? Yeah. In producing the first in producing the first 500 travel clocks per day is three 1003 $170. And that's do you final answer off given probe.