short1b - g x is shown below Use it to answer the following...

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Exam 1, Form B M170-007 Fall, 2010 Name: (1 pt.) Show all your work. Regardless of your prior experience with calculus, you must use limit methods for all derivatives on this exam. 1. (15 pts.) A moving object has position (in meters) given by f ( t ) = 5 t 2 - 3 t , with t in seconds. Find its position when its velocity is - 8 m/s. 2. The number of mice in a ±eld, P , is a function of time t (in months) as shown at right. (a) (5 pts.) Compute Δ P on the interval [0 . 5 , 1]. (b) (5 pts.) Compute Δ P Δ t on the interval [0 . 5 , 1]. (c) (5 pts.) On the graph, sketch a secant line that corresponds to your answer to (b). (d) (10 pts.) Compute P (0 . 5). Show all work. P (mice) t (months) 1
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3. (10 pts.) Suppose that f ( x ) = 3 x . Compute f (5). 4. (10 pts.) Compute lim h 0 5 + h - 5 h . 5. (10 pts.) The graph of a function f ( x ) = - x 2 + 4 x - 1 is shown at right, along with a tangent line. Given that the y -intercept of the tangent line is 1 . 25, locate the x -coordinate of the point of tangency. HINT: f ( x ) = - 2 x + 4 f x 2
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6. The graph function
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Unformatted text preview: g ( x ) is shown below. Use it to answer the following questions: (a) (5 pts.) At what points (if any) is g discontinuous? (b) (5 pts.) At what points (if any) is g non-diFerentiable? (c) (5 pts.) At what points (if any) is g ′ ( x ) = 0? (d) (5 pts.) On the axes immediately below the graph of g , sketch a graph of g ′ ( x ). g x g ′ x 3 7. (10 pts.) The temperature, T , of a cooling object is a function of time, x , as shown in the following table: x (minutes) 5 10 15 20 25 T ( ◦ C)-7 6 11 15 18 (a) Estimate the value of T ′ ( x ) for times x = 5, 10, 15 and 20 minutes. Write your answers in the table below. Be sure to include correct units. x (minutes) 5 10 15 20 T ′ ( x ) ( ) (b) T ′ is a function. Compute the derivative of T ′ at time x = 15 minutes. Your answer must include correct units. 4...
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short1b - g x is shown below Use it to answer the following...

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