M408Cprac2d - points. Find the intervals where the curve is...

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Math 408C Sample Test No Calculators, books, notes, etc. 1. Sketch a good graph of y = x 4 - 8 x 3 +18 x 2 , showing all critical points, inflection points, etc. 2. Sketch a graph of y = x 2 x 2 + 1 . Show everything. 3. Find the volume of the largest right circular cylinder which can be inscribed in a sphere of radius 10. 4. Two sides of a triangle have lengths 5 and 7, respectively. The angle θ between them is increasing at the rate of 1/2 radian per second. How fast is the length of the other side changing when θ is π/ 6? ( Hint: Law of cosines. ) 5. Use a linear approximation to estimate 3 29. 6. Find lim x →-∞ ( x + p x 2 + 2 x ) . 7. Sketch a good graph of y = x 2 (2 x 2 - 9), showing all critical points and inflection
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Unformatted text preview: points. Find the intervals where the curve is increasing, decreasing, concave up and concave down. 8. Sketch a good graph of y = x 2-x + 1 x , showing all critical points and inection points. Find the intervals where the curve is increasing, decreasing, concave up and concave down. 9. Find dy/dx if x y = tan( x 2 + y 2 ) 10. Find lim x tan2 x sin 3 x . 11. Find the absolute minimum and absolute maximum values of f ( x ) = 2 x 3-3 x 2-12 x + 1 on the interval [-2 , 3]. 12. Find all the critical points of f ( x ) = x 1 / 3-x-2 / 3 ....
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