Please show step-by-step solutions for me to understand. I need to be able to understand how to solve this problem so please make it step-by-step. I will appreciate it. Thank you so much! Have a great day ahead!

The price p (in dollars) and demand x for a product are related by a2 + 2xp + 25p2 = 74500. . If the price is increasing at a rate of $2 per month when the price is $30, find the rate of change of the demand. . If the demand is decreasing at a rate of 6 units per month when the demand is 150 units, find the rate of change of the price.Find the values of a. and b so that an) : 33 + mm\" + a: + b has an inection point at (7, 1) . [Express answers In fraction form when applicable. E.g., 3/4 for three'fourths, or -2/5 for negative two- fths.) b: Find the values of a and b so that f(x) = ax + 9x + b has a local minimum at A Q = b = (Express answers in fraction form when applicable. E.g., 3/4 for three-fourths, or -2/5 for negative two- fifths.)