Answer:
h(7) = 29
h'(7) = 44
Step-by-step explanation:
If [tex]h(x) =4f(x)+3g(x)[/tex], to find h(7) we can substitute the values of f(7) and g(7) and we get:
[tex]h(7)=4f(7)+3g(7)\\h(7)=4(5)+3(3)\\h(7)=20+9\\h(7)=29[/tex]
To find the derivative, we know that the derivative of a sum of functions equals the sum of the derivatives of those functions.
This would mean that [tex]h'(x)=4f'(x)+3g'(x)[/tex], we can substitute the values for f'(7) and g'(7)
[tex]h'(7)=4f'(7)+3g'(7)\\h'(7)=4(8)+3(4)\\h'(7)=32+12\\h'(7)=44[/tex]
