Looking through my old calc notes, I am reading that f(x) needs to be continuous on [a,b] and f ' (x) also needs to be continuous on [a,b]. Both conditions are needed. If you had to pick just one, then I'd say f(x) being continuous is much more important. Though I'm not 100% sure on this one. My thinking is that if there was any discontinuities on f(x), then the arc length would be distorted and overblown. The arc length should not account for any piece that isn't on the curve.
(0,3)
Please see the photo I added, if you do not understand, specify in the comments
Answer:
The p -value is less than 0.001.
Step-by-step explanation:
Given information:
Sample size = 25 chips
Sample mean = 985
Sample standard deviation = 10
Let as assume that sample is distributed normally.
The formula for test statistic

where,
is sample mean
μ is population mean.
s is sample standard deviation.
n is sample size.
The value of test statistic is



The p-value is

Therefore the p -value is less than 0.001.