## anonymous 4 years ago 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.

1. anonymous

just differentiate and let x=0. $$g'(0) = a sec^2 (0) +f'(0)$$ where $$sec^2(0)=1$$, so, $$g'(0) = a +3$$

2. anonymous

Can you help me with the second part too? 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. please?

3. anonymous

sure...for this question, you too find the h'(0) to get the gradient at that pt, but this time you also have to evaluate h(0) to get the point(0,h(0)) $$h'(0)=k \cos (0) f(0) + f'(0) sin(0)$$ $$h'(0)=-2k$$

4. anonymous

Thank you sooo much! I highly appreciate it :)

5. anonymous

you're welcome:)