One of the MC no calc questions was "what is the absolute minimum value on the interval 0 to (I forget). They gave you f(x) which was just a quadratic. Some of the choices were 0, 8, 13, 20… Sorry if that isn’t a good description but was the answer zero (choice A)
F’ cannot equal zero I stand by it
@AmandaEK was #2 the pipe one?
Owait was it the R and S one
Incorrect. The answer is -sin(x) graph and this is because the definition of a derivative states as the limit of h approaches 0 of f(x+h) - f(x) divded by h. However, in this problem our H value is already so small so it can be implied that we do actually have a “limit as h approaches zero” so now we know it’s just asking: what is the derivative of cos(x)? That is -sin(x).
@stoopidfoose yes the pipe one. It was the integral expression you didn’t need to evaluate
You want what the question was asking? Find the time at which the amount of water in the pipe is at a minimim
f(a) and f(b) can get infinitely close to each other in value BUT they can never equal each other. If the slope of the tangent line is 0 at a single point f(b) is still > f(a).
This is what you said. Now, you pretty much just said that “they can never equal each other”. the tangent line can only equal 0 when f(a) = f(b). This is actually a part of Roll’s Theorem. Anyway, you sorta disproved your point.
yeah bro we’re right
What did u guys get for the last question the entire test with d^2y??
@AmandaEK I think I said it was the integral of whatever the interval endpoints were as limits of the F(t) - D(t) or something like that. I’m not entirely sure I even remember what the question was.
1/32 @mattcinnamo
yeah but if they can get infinately close, then its not just the slope cant be zero, but it HAS to be increasing as well. I feel like their both true…
@Javacash01 The slope of the tangent line can still be 0 even if the value of the endpoints of an interval aren’t equal.
that’s not what i was saying!! go back and read exactly what i said. if you still don’t get it, i will refer you to a site.
http://tutorial.math.lamar.edu/Classes/CalcI/MeanValueTheorem.aspx
look at Roll’s theorem! read carefully what it is saying and you will realize that it basically disproves option A
I need to stay off of this website because I now think that I got every single question wrong
@Javacash01 No, it doesn’t. Rolle’s theorem says that there must be at least one c in [a, b] where f’© = 0 if f(a) = f(b). It doesn’t say that f’© = 0 only when that condition is met.
@RHSclassof16 I don’t know if that question about all values on the interval [0,5] that f(a)<f(b) and 0<a<b<5 could be the answer A. Since a and b are really intervals between 0 and 5, couldn’t some values in the interval a have f’(x)<0 but just increases after to have the b values greater than a?
I eliminated A because of that.
it’s true that there can be other situations where f prime of c can still be 0 but i’m telling u A is still not right lol.
YOU HAVE TO UNDERSTAND THAT A AND B ARE LOCATED SOMEWHERE IN THE OPEN INTERVAL! IT’S AN OPEN INTERVAL AND IN THAT OPEN INTERVAL F(B) IS ALWAYS GREATER SO THE SLOPE WILL NEVER BE ZERO IN THE INTERVAL!