Question

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.

Answer 1

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

Answer 2

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?

Answer 3

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))
\(h'(0)=k \cos (0) f(0) + f'(0) sin(0)\)
\(h'(0)=-2k\)

Answer 4

Thank you sooo much! I highly appreciate it :)

Answer 5

you're welcome:)