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MA 121 ASSIGNMENT 2b

MA 121 ASSIGNMENT 2b - MA 121 ASSIGNMENT 2 Please show all...

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MA 121 ASSIGNMENT 2 Please show all of your work in answering the following: 1. Let f ( x ) = x 3 + 6 x 2 + 9 x a) Find the intervals on which f is increasing or decreasing. b) Identify all relative extrema c) Find the intervals on which f is concave up or concave down d) Sketch the curve 2. Find the absolute maximum and the absolute minimum of f ( x ) = x 2 6 x + 9 on the interval [ 1, 6 ]. 3. Sketch the graph of f ( x ) = x 2 + 1 x , identifying relative extrema, inflection points, asymptotes, etc. 4. Find y when a) y = 5 + x 2 e x b) y = e 2 x 3 2 x + 1 c) y = ( e 3 x + 2) 5 d) y = 2ln7 x e) y = ln x 2 + 1 x + 2 f) y = 7 3 x g) y = x 4 4 x h) y = ln( x 4 3 x 2 ) ( x 5) 3 5. The half life of cobalt-60 is 5.3 years. a) Find its decay rate. b) If you initially have 20 grams of this material, how long until only 15 grams remain? 6. An open box is to be constructed from a piece of cardboard that is 30 in. by 30 in.
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