True or False Questions: 1)If a function is continuous at a point a, then the fu

Question

True or False Questions: 1)If a function is continuous at a point a, then the function is differentiable at a. 2) If a function is differentiable at a point a, then the function is continuous at a. 3)If f(1) > 0 and f(3) < 0, then there exists a number c between 1 and 3 such that f(c) = 0. 4) If s(t) is the position function of an object, then s ''(t) is its velocity function. 5) 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)If f '(x) < 0 for 1 < x < 6, then f(x) is decreasing on (1, 6). 8)If f ''(x) = 0 at the point x = c, then c is a point of inflection. 9)The most general antiderivative of f(x) = x^-2 is F(x) = -1/x + C

Explanation / Answer

1)false there can be a sharp corner at that point 2)true differentiability implies continuity always 3)false as continuity of the function is not mentioned 4)false it will be acceleration function 5)true 6)false it is not neccessary but converse is true 7)true 8)true 9)true

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