UFCalcSet14 - A ( t ) of the second liquid are measured,...

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Exercises UF Calculus Set 14 1. Find the derivative of the function in two different ways. Once with product or quotient rule, and once without. (a) f ( x ) = x ( x + 2) (b) f ( x ) = x + x x 2 2. Find the derivative of the given function. (a) f ( x ) = 2 - 3 x 1 + 2 x (b) f ( v ) = v (1 - e v ) (c) f ( x ) = 1 1 + xe x (d) f ( x ) = x 4 - x (e) f ( x ) = x 2 / 3 1 + x 2 (f) f ( x ) = e x 5 - x 3. For each function in Exercise 2 above, write all x -values (if any) at which the tangent line to the graph would be horizontal. 4. Find the second derivative of the function. (a) f ( x ) = x 2 + x 2 (b) f ( x ) = (1 - x 2 ) e x 5. Find the equation of the tangent line to the curve at the given point: (a) y = ( x - 2) - 1 at the point (1 , - 1) .. (b) y = xe x at the point (0 , 0) . (c) y = xe x at the point (1 ,e ) . 6. A tank containing water and a second liquid is monitored every hour. The total volume V ( t ) of liquid in the tank as well as the amount
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Unformatted text preview: A ( t ) of the second liquid are measured, along with their rates of change with respect to time t in hours. At which time(s) below is the concentration of the second liquid: (a) decreasing? (b) changing at the fastest rate (speed)? What is the rate? (c) changing at the slowest rate (speed)? What is the rate? 7. Examine the table above without context. Find the value of the derivative of each of the following functions at t = 1 , 3 : (a) V ( t ) A ( t ) (b) A ( t )-V ( t ) (c) t 2 A ( t ) (d) [ V ( t )] 2 (Note. .. this is V ( t ) V ( t ) ) (e) 2 t + A ( t ) 1 + V ( t ) (f) V ( t ) e t -...
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UFCalcSet14 - A ( t ) of the second liquid are measured,...

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