List the THREE things you need to check to verify that a function is continuous

Question

List the THREE things you need to check to verify that a function is continuous at a number Find the points at which the following function is NO T continuous, and explain why. Use one of the limit definitions of the derivative (either f'(a) or f'(x) to find f'(2) for the following function. f(x) = Find the first and second derivatives. You do not need to simplify your answer. f(x) = +5/3x6 Find dy/dx. Simplify the numerator of your answer. y = 2x5 + 8/3x4 -6x + 7 Differentiate. You do not need to simplify your answer. y = (5u8 + 6u - 7)(9u10 - 11u + 12) Find the equation of the tangent line to the curve at the point with the given x-coordinate. y = 3x5 - 7x + 9 x = 1 The position function is given below. Time is in seconds and distance is in meters. Find the velocity and acceleration. What is the acceleration when the object is at rest? (Use appropriate units) s(t) = t3 - 7t2 + 8t -5

Explanation / Answer

4....points are x = 0 and 2....

5.... f'(2) = 2/13.......

10......v(t) = 3t^2 - 14t + 8....

a(t)= 6t - 14....

acceleration when object at rest is a = 10......

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