4.1 – Solving Polynomial Equations
4.2 – Solving Linear Inequalities
4.3 – Solving Polynomial Inequalities
4.4 – Rates of Change in Polynomial Functions
Mixed!
100
Find the roots of y = (x+5)(x^2-4x-12)
x = -5, -2, 6
100
solve (x + 3) (x - 4) < 0
when x E [-3, 4] OR -3 < x < 4
100
solve (x + 2) (x - 3) (x+ 1) > 0
x > 3 or -2 < x < -1 OR [-2, -1] U [3, oo)
100
Given the graph P(x) list all the intervals where the average rate of change will be positive, negative or zero
What is positive: [-1.5, 0.2] , [1.3, 2.3] What is negative: [-2.2, -1.6] , [0.2, 1.3] What is zero: [-2, -0.7], [-0.7, 1], [-2, 1], [-2,1.6], [-0.7,1.6], [-0.7,1], [1, 1.6]
100
solve 9x4 - 42x^3 + 64x - 32 = 0
x = 2, 4/3
200
Solve for x given 0 = (x^2-2x-24)(x^2-25)
x = -4, 6, 5, -5
200
solve 2x (x + 4) - 3 (x + 4) < 0
when x E [-4, 3/2] OR -4 < x < 3/2
200
solve x^3 - 9x - 1 < -x^2 + 8
when x E (-oo, -3]
200
Consider the function f(X) = 2 (3x - 4)^2 - 6. Determine the average rate of change on the following interval 6 < x < 11
The answer is approximately 335
200
without a calculator, explain why the inequality 2x ^24 + x^4 + 15x^2 + 80 < 0 has no solution.
Since all the powers are even and the coefficients are positive, the answer for the polynomial on the left will always be positive.
300
solve for x given, 2x^3 + 3x^2 = 5x + 6
x = -2, -1, 3/2
300
Write an inequality for <-----.(-2)--------------->
x > -2
300
solve x^2 - 6x + 9 > 16
x < -1 or x > 7 OR when x E (-oo, -1] U [7, oo)
300
Given g(x) = x^2 - 3x - 8. Find the instantaneous rate of change at x = 5. Find Iroc using two calculations with h=0.01 and h=0.001
The answer is approximately 7
300
solve (x+1)(3x-1)(x-16) = 0
x = -1, 1/3, 16
400
An open topped box is made from a rectangular piece of cardboard, with the dimensions of 24cm by 30cm, by cutting congruent squares from each corner and folding up the sides. Find the dimensions of the squares to create a box with a volume of 1040cm ^ 3
2cm by 2cm or 7.3cm by 7.3cm
400
Solve 2x < (3x+6)/2 <(less than or equal too sign) 4+2x
when x E [-2,6]
400
f(x) = 2x^3 - x^2 +3x +10 and g(x) = x^3+3x^2 +2x +4 Determine when f(x) < g(x)
when x E (-oo, 1)
400
the graph P(x) is given. Calculate the average rate of change in p(x) on the interval -2 < x < 0
the answer is 1/2 or 0.5
400
Chris makes an open-topped box from 30 cm by 30 cm piece of cardboard by cutting out equal squares from the corners and folding up the flaps to make the sides. What are the dimensions of each square, to the nearest hundredth of a centimetre, so that the volume of the resulting box is 1000cm^3.
10cm by 10cm or 1.34 cm by 1.34cm
500
Solve 6x^4 -13x^3 -29x^2 + 52x = -20
x = +- 2, x = -1/3, x = 5/2
500
A phone company offers 2 deals. The first plan is unlimited calling for a $35.00 a month. The second plan is a monthly fee plus $0.05 per minute. When is the unlimited plan a better deal?
x > 300 It is a better deal if you call more than 300 minutes a month
500
Determine where the intervals of the function are positive and negative given f(x) = 4x^3 +36x^2 + 4x -44
f(x) is positive [-8.75,-1.25] U [-1.25,1] f(x) is negative [-oo, -8.75] U [1,oo]
500
A company has been manufacturing toy monkeys since the year, 2000. The growth in toys can be modelled by function m(x) = 5(2x+100) ^ 2 + 10000. a) at what rate is number of toys being manufactured changing between the years 2005 and 2010? b) at what rate is number of toys being manufactured expected to be in 2013?
a) 30 500 toys are being manufactured during the years 2005 and 2010 b) 3320 toys are being manufactured at the beginning of 2013
500
Consider the function f(x) = e ^ x (e is called Euler's Number where e = 2.7183) a) Find f(6) and the instantaneous rate of change at x = 6. b) Repeat part a) with three more x-values c) What can you conclude from your findings? What is the relationship between f(x) = e^x and instantaneous rate of change?
a) approximately 403.44 b) answers will vary c) the instantaneous rate of change of e ^ x for any value of x is relatively close to e ^ x
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