Summarizing the distributional derivative of a piecewise smooth function. this exercises generalizes (and summarizes) many of the previous exercises and examples. suppose f is a c1 (continuously differentiable) function except at a point xo. define the function g(x) = 10 if r + xo if x = to. a) if f is continuous at x = xo, prove (show) that f' = g in the sense of distributions. b) suppose f has a jump discontinuity at xo with a = lim f(x) and b = lim 2+25 f(x). +20 show that f' = g + (b − a)& go in the sense of distributions.

Someone answer asap for ! a discount store’s prices are 25% lower than department store prices. the function c(x) = 0.75x can be used to determine the cost c, in dollars, of an item, where x is the department store price, in dollars. if the item has not sold in one month, the discount store takes an additional 20% off the discounted price and an additional $5 off the total purchase. the function d(y) = 0.80y - 5 can be used to find d, the cost, in dollars, of an item that has not been sold for a month, where y is the discount store price, in dollars. create a function d(c(x)) that represents the final price of an item when a costumer buys an item that has been in the discount store for a month. d(c(x)) =