Question

Help with calc please?
The twice–differentiable function f is defined for all real numbers and satisfies the following conditions:

f(0)=3

f′(0)=5

f″(0)=7


1. 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.
2. The function h is given by h(x)=cos(kx)[f(x)]+sin(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

Answer 1

if \( g(x)=e^{ax}+f(x) \)
then \(g'(x) = ???\) and \(g''(x) = ???\)

Answer 2

would g'(x)=ae^ax +f'(x)?

Answer 3

I understood the first question and finished it but I still need help with the second one.

Answer 4

I finished the problems, thanks for the clue on the problems!

Answer 5

cool, well done

and yes

if
\(g(x) = e^{ax} + f(x)\)

then
\(g'(x) = ae^{ax} + f'(x)\)

and
\(g''(x) = a^2e^{ax} + f''(x)\)