Tutorial7.pdf

UNIVERSITI PUTRA MALAYSIA

FAKULTI SAINS


MTH 3004 PENGENALAN KEPADA MATEMATIK EKONOMI DAN PERNIAGAAN
Tutorial 7
1. Find the derivative for each function
(a) y=( x3 − 2 x 2 + 5)( x 4 − 3 x 2 + 2) (b) f( x ) = 3 x5 ln 5 x
4x 3e2t
(c) y = (d) f( t ) =
x2 −1 4t 2 − 3
3x− 6 x
(e) f (x) = (x2 + 3)(x3 − 3x + )1 (f) y =
5x2 − 2

2. Find the derivative for each of the following functions using chain rule.
(a) f (x) = (x3 −)1 2 (b) f (x) = x5 x3 + 2
6 (x3 + )4 5
(c) f (x) = (d) f (x) =
x2 + 4 5x +1

3. Determine whether the relative maximum and/or minimum occurred using first
derivative test.
(a) y = x 4 − 2x 2 (b) y = 3x5 − 5x3

4. Test for the relative maximum and minimum using the second derivative test.
1
(a) y = x 2 − 5x + 6 (b) y = x3 + 2x 2 − 5x +1
3

5. Sketch the graph of the function y = x3 − 9x 2 + 24x −19 by determine the relative
maximum and minimum, inflection point, x and/or y-intercept, and it’s ultimate
direction.

6. If r = q(20 − q) is total revenue function. Find the marginal revenue function.

7. If c = .0 0001q3 −.0 02q 2 + 3q + 6000 is a total cost function, find the marginal cost
when q = 100.

q +12
8. If p = is