AP+Review+7+Question+14

Review 7 14. The twice differentiable function //f // is defined for all real numbers and satisfies the following conditions: f(0) = 2, f '(0) = - 4, and f "(0) = 3. (a) The function //g // is given by g(x) = e^(ax) + f(x) for all real numbers, where //a// is a constant. Find g '(0) and g "(0) in terms of //a//. Show the work that leads to your answers. (b) The function //h //is given by h(x) = cos(kx) f(x) for all real numbers, where //k// is a constant. Find h '(x) and write an equation for the line tangent to the graph of //h //at x=0.