1337Exam3solutions

# 1337Exam3solutions - iii Find all inflection points of N B...

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30 I ~-tr 0 oJ Math 1337 Section 4 T. Hagstrom . .- Spring 2009 Exam 3 There are 4 problems each worth 25 points plus a fifth problem for extra credit. Show all your work. Good luck! 1. Let ex f (x) = ex + x2 i. Find all critical points of f. ii. Find all intervals of increase or decrease. iii. Find all local maxima and minima. iv. Compute lim,,, f (x) and lim,,-, f (x).

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where a > 0 and p are constants: the standard deviation and mean respectively. 1 The I i. Find all critical points of N. be \ \ GkrVt , u ii. Use the second derivative test to classify these as local maxima or minima. 145- 2. The normal density function is defined by: N(x) = 7 - r

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Unformatted text preview: iii. Find all inflection points of N. - B P t r iv. Find intervals of increase and decrease and intervals of upward and downward concav- ity. v. Sketch the graph of N. L. 4. The acceleration of a particle is given by: Supposing its initial position is 0 and its initial velocity is 0 write down a formula for its position, x ( t ) . Show that for t > 2 the velocity is always positive. 3. Find the dimensions and area of the rectangle of largest area whose base is on the x-axis and whose other two vertices are above the x-axis and lie on the parabola y = 18 - 2x2. 5. (Extra credit) Use the Mean Value Theorem to prove the following inequalities: 1. . -...
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1337Exam3solutions - iii Find all inflection points of N B...

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