Question

TRUE OR FALSE: If f '(2) = 3.1 and g '(2) = 7.3, then the graph of f(x) + g(x) has slope 10.4 at x = 2.

Answer 1

h(x) = f(x) + g(x)
h(2) = f(2) + g(2)

Answer 2

recall the limit properties?
\[\lim_{x \rightarrow a}[f(x) \pm g(x)]=\lim_{x \rightarrow a}f(x) \pm \lim_{x \rightarrow a}g(x)\]

Answer 3

you can say the derivatives add from that

(f + g) ' = f ' + g '

Answer 4

h'(2) = f'(2) + g'(2)
substitute f'(2) with 3.1 and g'(2) with 7.3