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Section 2.5: Problem 10 (1 point) Previous Problem Problem List Next Problem If f ( t ) = 8t - , find f'(t).Section 2.5: Problem 11 (1 point) Previous Problem Problem List Next Problem -3x Let f(x) = Then, V9 - 7: f'(x) =Section 2.5: Problem 12 (1 point) Previous Problem Problem List Next Problem Let y = (5 + cos x)". Then, dySection 2.5: Problem 13 (1 point) Previous Problem Problem List Next Problem Find an equation of the tangent line to the curve y = sin(3x) + cos(6x) at the point ( #, y(#)). Tangent line: y=Section 2.5: Problem 14 (1 point) Previous Problem Problem List Next Problem Let f(x) = 2x' cos(6x). Then, f'(x) = f' ( 2 ) = f"(x) = f"(2) =Section 2.5: Problem 15 (1 point) Previous Problem Problem List Next Problem A table of values for f, g, f', and g' is given below. f(I) g(x) f'(1) 9(x) 1 2 2 3 1 2 3 1 3 1 3 3 1 1 (A) If h(x) = f(g(x)), then h'(3) = (B) If H(x) = g(f(x)), then H'(2) =Section 2.4: Problem 16 (1 point) Previous Problem Problem List Next Problem Note: You can click on the graph to obtain a larger version in a new browser window. The graphs of the function f (given in blue) and g (given in red) are plotted above. Suppose that u(x) = f(x)g(x) and v(x) = f(x)/g(x). Find each of the following: u'(1) = 2 v'(1) =Section 2.4: Problem 16 (1 point) X Previous Problem Problem List Next Problem 6 Note: You can click on the graph to obtain a larger vel The graphs of the function f (given in blue) and g (given i )g(x) and v(z) = f(z)/g(x). Find each of the following: u'(1) = v'(1) = -1 1:0 -1Section 2.5: Problem 17 (1 point) Previous Problem Problem List Next Problem A Cepheid variable star is a star whose brightness, B, alternately increases and decreases. Suppose that Cephei Joe is a star for which the interval between times of maximum brightness is 6.8 days. Its average brightness is 2 and the brightness changes by +/-0.5. Using this data, we can construct a mathematical model for the brightness of Cephei Joe at time t, where t is measured in days: B(t) = 2 + 0.5 sin(2xt/6.8) (a) Find the rate of change of the brightness, in units of brightness per day, after t days. Rate of change = (b) Find the rate ofchange of increase, in units of brightness per day, after one day. Rate of change of increase =Section 2.5: Problem 18 (1 point) Previous Problem Problem List Next Problem Find the 23 " derivative of y = cos(2x ) by finding the first few derivatives and observing the pattern that occurs