1. True or False: If a function is continuous at a point a, then the function is
ID: 3288505 • Letter: 1
Question
1. True or False: If a function is continuous at a point a, then the function is differentiable at a.
2. True or False: If a function is differentiable at a point a, then the function is continuous at a.
3. True or False: If f(1) > 0 and f(3) < 0, then there exists a number c between 1 and 3 such that f(c) = 0.
4. True or False: If s(t) is the position function of an object, then s ''(t) is its velocity function.
5. True or False: Newton is credited for the Fundamental Theorem of Calculus.
6. True or False: If f '(c) = 0, then f(x) has a local maximum or minimum at c.
7. True or False: If f '(x) < 0 for 1 < x < 6, then f(x) is decreasing on (1, 6).
8. True or False: If f ''(x) = 0 at the point x = c, then c is a point of inflection.
9. True or False: Let f be continuous on [a, b]. If x varies between a and b, and g(x) =Integral (x,a) f(t) dt, then g '(x) = f(x).
10. True or False: The most general antiderivative of f(x) = x^?2 is F(x) = ?1/x + C.
Explanation / Answer
1. False. Take f(x) = |x|, which we know is not differentiable at x = 0 but is continuous there.
2. True.
3. False, that's only true if f was continuous.
4. False, s''(t) would be the acceleration function; not the velocity function.
5. True, him and Leibniz.
6. True
7. True
8. True
9. False, g'(x) = -f(x)
10. True.
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