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1 / 2 - 100% + 8 Pert | Log | 3 Stut ( x ) Unt | 23 Cou | 3 Cou | M UC | Res | M Cak | M de | @) point. 1) If possible, give an example of where a function is differentiable at a point but not continuous at that pedia/1185000_1185500/1185018/61428cba45829421debbff2d952aad7ec49c508/1185018.pdf Q 2 / 3 - 90% + H O point. 2) If possible, give an example of where a function is continuous at a point but not differentiable at that 7) An object in free fall has its distance from the ground measured by the function d(() = -4.9t* + 50, where d is in meters and t is in seconds. If gravity is the only acceleration affecting the object, what is gravity's constant value (include units in your answer)? ) Without a graph, how can one show differentiability of a function at a point? tomain. 3) The graph of y = f(x) is shown below on the domain [0, 5]. Sketch the graph of y = f"(x) on the same ) Where is the function g(x) = 3x- x + 5 differentiable? 5) Explain why the definition of a numerical derivative does not exist at x = 2 in the graph shown. derivatives? 9) If a function is decreasing with an upward concavity. what do you know about the function's first two interval [0, 4]. 10) Use the graph of y = /'(x) shown below to describe the concavity in the graph of y = f (x) on the Log | 3 Stu ( x ) Unt | 23 Cou | 3 Cou | MUC | Res | M Cak | M de | (@) se. ) Explain why the definition of a numerical derivative de 1185000_1185500/1185017/dc60a9bef2d76c406295a9bbb70a038f2579e9b/1185017.pdf 1 / 2 - 100% + 1) Find dy giv "dx given y? = x. ) Determine if the function f(x) = * * is differentiable at x = 1. 2JX. X21 2) Find the tangent line to y? = x at the point (4, -2). ) Determine if the function g(x) = *+1 x1 3) Find given 3xy = In x. 9) Where is the function hit) - (t +5)"> differentiable? 4) Find for the circle defined by the equation x2 + y? = 18. I 0) Determine if the function y(x) - -x xso 3x, x> is differentiable at x = 0. 5) The circle defined by the equation x" + y" = 18 has two points where the slope of its tangent line is m = 1. Find those points. (Hint: One technique is to solve a system of equations using the circle and slope equations.) day given e ) = y? + x. Log | 13 Stut ( x ) Unt | 3 Cou | 3 Cou | M UC | Res | M Cake | M de | (@) 1185000_1185500/1185017/dc60a9bef2d76c4806295a9bbb70a038f2579e9b/1185017.pdf 1) Find the second derivative of f(x) = 24Vx 2 / 2 | - 100% + . 2) If y = cos x, what is y (x)? 7) Find given y = logz (6x + x). 3) Find - (613 +21-9) 8) Find for the hyperbola defined by the equation y? - x? = 7. 4) Find the third derivative of g(x) = e". 9) Find the slope of the tangent line to the hyperbola defined by the equation y? - x2 = 7 at the point (3, 4). 5) An object moves along a line according to the position function x(() = 3 + 2 - t*. Find the acceleration function. 10) Find the value of for the hyperbola defined by the equation y? - x? = 7 at the point (3, 4). (Hint: You can use the information regarding from the last exercise.) 6) A weight oscillates in a vertical motion according to the position function y(f) = -5 cos t. Assuming t 2 0. when will the acceleration of the weight be zero for the first time