1. Consider the following table for the functions f (x) and g (x). X f(x) g(x) f(x) g'(x) -1 -2 4 2e 1 2 2 -1 e 3 If h(x) = e - 28(rf(*))then find h'(1). Give exact answer only. 1 2. Find f(0) for / (x) = x + 1 VX+18. The number of yeast cells in a laboratory culture increases rapidly initially but levels off eventually. The population is modeled by the function 1 + bg -0.7t where t is measured in hours. At time t = 0 the population is 30 cells and is increasing at a rate of 12 cells/hour. Find the values of a and b. According to this model, what happens to the yeast population in the long run? 9. Suppose we know that f(1) = f'(1) = 1. Define g(x) = f(x3). Use linear approximation to estimate the value of g (1.1). 10. A window has the shape of a square surmounted by a semicircle. The base of the window is measured as having width of 60 cm with a possible error in measurement of 0.1 cm. Use differentials to estimate the maximum error possible in computing the area of the window. 11. Use differentials to estimate the amount of paint needed to apply a coat of paint 0.05 cm thick to a hemispherical dome with diameter 50 m. Give answer in m BONUS QUESTION: Suppose f is a differentiable function such that f(g(x)) = x and we also have f'(x) = 1+ [f(x)]]. Find g'(x)