Question

If ƒ(x ) = 3x + 1, then ƒ(a + h ) - ƒ(a ) =

Answer 1

Hello,

f(a+h)=3(a+h)+1=3a+3h+1
f(a)=3a+1
f(a+h)-f(a)=3a+3h+1-(3a+1)=3h
$\lim_{h \to 0} \frac{f(a+h)-f(a)}{h}=\lim_{h \to 0}\frac{3h)}{h}=3$

f'(x)=3