Final answer:
For this problem, we are given specific values of functions at x=3 and their derivatives. By using these values, we can find the values of different expressions involving the given functions.
Step-by-step explanation:
a) f′(3)+g ′(3): To find the value of f′(3)+g ′(3), we simply add the value of f′(3) and g ′(3). Given that f′(3) = 9 and g ′(3) = 6, the sum is 9 + 6 = 15.
b) f(3)⋅g(3): To find the value of f(3)⋅g(3), we multiply the value of f(3) and g(3). Given that f(3) = 5 and g(3) = -1, the product is 5 ⋅ -1 = -5.
c) f(3)⋅g ′(3): To find the value of f(3)⋅g ′(3), we multiply the value of f(3) and g ′(3). Given that f(3) = 5 and g ′(3) = 6, the product is 5 ⋅ 6 = 30.
d) f(3)+g(3): To find the value of f(3)+g(3), we simply add the value of f(3) and g(3). Given that f(3) = 5 and g(3) = -1, the sum is 5 + (-1) = 4.