# Tutorial 6 - x for the prescribed value x 13 1 3 2 4 = x x...

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Tutorial 6 – Introduction to Calculus and Linear Algebra Page 1 of 1 Tutorial 6 Introduction to Calculus and Linear Algebra In Exercises 1 to 8, compute the derivative of the given function by first principle and then find the slope and equation of the line that is tangent to its graph for the specified value of the independent variable. 1. 3 5 ) ( - = x x f at x = 2 2. 5 3 2 ) ( 2 - - = x x x f at x = 0 3. t t g 2 ) ( = at t = 1/2 4. x x f = ) ( at x = 9 5. 2 ) ( x x f = at x = 1 6. x x f 2 7 ) ( - = at x = 5 7. x x f 2 ) ( - = at x = –1 8. x x f 2 ) ( = at x = 4 In Exercises 9 to 12, differentiate the given function. Simplify your answers. 9. 3 3 1 ) ( x x x f + = 10. 3 3 1 2 16 ) ( 2 2 / 3 2 x x x x x x f + + - + - = 11. 3 2 5 4 2 1 2 2 3 / 2 2 + + + + + + - = x x x x x y 12. 3 2 5 4 x x x y - - = In Exercises 13 to 15, find the rate of change of the given function f ( x ) with respect to
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Unformatted text preview: x for the prescribed value x . 13. 1 3 2 ) ( 4 + + = x x x f at x = –1 14. 2 1 ) ( x x x x f +-= at x = 1 15. x x x x f + = ) ( at x = 1 16. An environmental study of a certain suburban community suggests that t years from now, the average level of carbon monoxide in the air will be 4 . 3 1 . 05 . ) ( 2 + + = t t t Q parts per million (ppm). (i) At what rate will the carbon monoxide level be changing with respect to time 1 year from now? (ii) By how much will the carbon monoxide level change this year? (iii) By how much will the carbon monoxide level change over the next 2 years?...
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