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# Tutorial 11 - x 15 5 3 3 5 t t t f-= 2 ≤ ≤-t 16 1 u u u...

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Tutorial 11 – Introduction to Calculus and Linear Algebra Page 1 of 1 Tutorial 11 Introduction to Calculus and Linear Algebra In Exercises 1 to 7, determine where the given function is increasing and decreasing, and where its graph is concave up and concave down. Find the relative extrema and inflection points. 1. 2 9 3 1 ) ( 3 + - = x x x f 2. 10 4 ) ( 3 4 + - = x x x f 3. 3 ) 2 ( ) ( - = x x f 4. 3 2 ) 5 ( ) ( - = x x f 5. 3 ) 4 ( 2 ) ( + = x x x f 6. 1 ) ( 2 + = x x g 7. 1 1 ) ( 2 + + = x x x f In Exercises 8 to 13, use the second derivative test to find the relative maxima and minima of the given function. 8. 1 3 ) ( 2 3 + + = x x x f 9. 2 2 ) 9 ( ) ( - = x x f 10. x x x f 18 1 2 ) ( + + = 11. 2 2 ) 5 ( ) ( - = x x x f 12. 2 1 2 ) ( t t h + = 13. 2 3 ) 2 ( ) ( x x x f - = In Exercises 14 to 17, find the absolute maximum and absolute minimum (if any) of the given function on the specified interval. 14. ; 5 4 ) ( 2 + + = x x x f 1 3 -
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Unformatted text preview: x 15. ; 5 3 ) ( 3 5 t t t f-= 2 ≤ ≤-t 16. ; 1 ) ( u u u f + = > u 17. ; 1 1 ) ( + = x x f ≥ x 18. A carpenter has been asked to build an open box with a square base. The sides of the box will cost \$3 per square metre, and the base will cost \$4 per square meter. What are the dimensions of the box of greatest volume that can be constructed for \$48? 19. A truck is 300 miles due east of a car and is traveling east at the constant speed of 30 miles per hour. Meanwhile, the car is going north at the constant speed of 60 miles per hour. At what time will the car and truck be closest to each other?...
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