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.
Answer:
or approximately (0.544, 4.179)
Step-by-step explanation:
A function and its tangent lines intersect when their slopes are the same. Find the x-coordinate when the slope of f(x) is equal to 8/7 by taking the derivative of f(x):
Set 
equal to 8/7 and solve for x:
Therefore, 
will intersect at a point of tangency with a line of slope 8/7 at x=49/900. Plug in x=49/900 into to get the y-coordinate:
⇒Answer: (49/900, 3761/900) or approximately (0.544, 4.179)
Yes because when your multiply every thing together you’ll have 9/15 miles
Answer:
Step-by-step explanation:
Notice they both have the same slope of 3x so they are parallel, but different y intercepts. This means the lines never intersect and thus there are no solutions to the system of equations.
