Consider the following initial-value problem. y" - 3y' = 8e²t - 2e-t, y(0) = 1, y'(0) = −1 Find L{f(t)}, for f(t) = 8e²t - 2e-t. (Write your answer as a function of s.) 6s + 12 L(f(t)) = (s-2) (s+1) Use the Laplace transform to solve the given initial-value problem. y(t) = 8e²t - 2e

Find f. f ″(x) = 8x3 + 5,    f(1) = 5,    f ′(1) = 4

Samsung′s total revenue curve is R(q) = 126q + 40q2and its average cost isA(q) = q2 + 12q − 1233 −6930/q.a. State the name of the function derived when the average cost, A(q), andSamsung’s quantity, q, are multiplied.

If f(t) = /9t+1, find f"(5).

Find the slope of the graph of the function x2+y2=xy+1/4 at (1/2 , 1/2)

15. Identify y - intercept for f(x) = 2(x² - 5) + 4.

2. Find the x-intercepts for g(x) = 3x' -12x² - 36x

Find y as a function of tif with y(0) = 6, y(0) = 7. y= 400g"-729y=0

A factory can produce R rugs a month based on the function R(n) = 4n2 – 7n + 58, where n is the number of production lines that - are operational. The number of production lines that are operational is determined 15 by n(x) + 20x, where x is the number of managers overseeing a production line. What are the units when calculating the rate at which the rug production is changing when there are 4 managers to oversee the production lines?

Consider the function f(x)=x2+6(5x−10)(x+4)f(x)=x2+6(5x-10)(x+4). For each prompt below, if no solution exists - enter "DNE". If there is more than one solution, enter your answer as a comma-separated list (like "1, 3"). You may find it helpful to rewrite the numerator or denominator in a different form to help you complete some of the parts. Determine the vertical intercept of ff. f(0)=f(0)=    Determine the zeros (or "roots") of ff. x=x=    Determine the vertical asymptote(s) of ff. x=x=    Determine the horizontal asymptote of ff. y=y=