use f(x)=lim_{h→0} \\frac{f(x + h)-f(x)}{h} to find the derivative at x for the given function. s(x)=7x + 8…
use f(x)=lim_{h→0} \\frac{f(x + h)-f(x)}{h} to find the derivative at x for the given function. s(x)=7x + 8 s(x)=□
Answer
Explanation:
Step1: Find s(x + h)
Substitute x + h into s(x): s(x + h)=7(x + h)+8 = 7x+7h + 8
Step2: Calculate s(x + h)-s(x)
s(x + h)-s(x)=(7x + 7h+8)-(7x + 8)=7h
Step3: Calculate (\frac{s(x + h)-s(x)}{h})
(\frac{s(x + h)-s(x)}{h}=\frac{7h}{h}=7)
Step4: Find the limit as h→0
(s^{\prime}(x)=\lim_{h\rightarrow0}\frac{s(x + h)-s(x)}{h}=\lim_{h\rightarrow0}7 = 7)
Answer:
7