The twice-differentiable function f is defined for all real numbers and satisfies the following conditions: f(0)=...

 

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The twice-differentiable function f is defined for all real numbers and satisfies the following conditions: f(0)= -2, f' (0) = 3, f"(0) = -1. A. The function g is given by g(x) = tan(ax) + f(x) for all real numbers, where a is a constant. Find g'(0) and g" (0) in terms of a.(20 points) B. The function h is given by h(x) = sin(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. (10 points) The twice-differentiable function f is defined for all real numbers and satisfies the following conditions: f(0)= -2, f' (0) = 3, f"(0) = -1. A. The function g is given by g(x) = tan(ax) + f(x) for all real numbers, where a is a constant. Find g'(0) and g" (0) in terms of a.(20 points) B. The function h is given by h(x) = sin(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. (10 points)

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