Final answer:
The question requires finding the tangent line and a derivative evaluation for two mathematical functions, but due to the lack of specific details about the functions involved, it is not possible to provide an accurate answer.
Step-by-step explanation:
The student's question involves two separate parts: Part A, which asks for the equation of the tangent line for a certain function k|x| at x=4, and Part B, which asks for the derivative h'(3) of another function h(x) evaluated at x=3. For both parts, specific details and formulas from the provided contexts are required to compute the answer accurately.
In Part A, the general process would involve finding the derivative of the function k(x) at x=4, then using the point-slope form to write the equation of the tangent line. However, due to insufficient information regarding g(x) and f(x), an exact calculation cannot be made.
Similarly, for Part B, the calculation of h'(x) requires knowledge of the derivatives of f(x) and g(x), as well as simplifying the given expression for h(x). Without the explicit functions of f(x) or g(x), precise values for h'(3) cannot be determined.
Given the incomplete information, and in order to maintain accuracy and professionalism, it would be inappropriate to attempt to provide an answer to either part of the student's question.