Suppose that f(x) is a function with f(135) = 43 and f'(135) = 7. Estimate f(138). f(138) = ____

Differentiate the following function. f(x) = 6 +5x+4ex f'(x) =

Suppose the derivative of a function f(x) is df/dx = (x-8)(x+4)(x-3). Are the below values local minima, local maxima, or neither? x = -8 x = -4 x = 3 x = 12

The U.S. Energy Information Administration projected that imports of petroleum products in 2005 would be 4.81 quadrillion Btu and would increase by 5.47% each year through 2020.T (a) Find the function of the model that gives projected petroleum imports in quadrillion Btu, where t is the number of years since 2005, with data from 0 sts 15 P(t) = quadrillion Btu (b) According to the model, when will imports exceed 7 quadrillion Btu? (Round your answer for t to two decimal places.) Imports will exceed 7 quadrillion Btu in t= years which will occur in the year (c) Describe the end behavior of the model as time increases. P(t) increases without bound as t increases. O P(t) approaches a limiting value of 33.67 as t increases. OP(t) decreases without bound as t increases P(t) remains constant as t increases. OP(t) decreases toward 0 as t increases