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13. The concentration, C, of a drug injected into the bloodstream t hours
t
after injection can be modelled by C(t) 4 2t 2 . Determine when the
concentration of the drug is increasing and when it is decreasing.
4.2 Maximum and Minimum Values of a Polynomial
Function
14. Find the absolute maximum and minimum values.
(a) f (x) x 2 2x 6, 1 ≤ x ≤ 7
(b) f (x) x 3 x 2 , 3 ≤ x ≤ 3
(c) f (x) x 3 12x 2, 5 ≤ x ≤ 5
(d) f (x) 3x 5 5x 3 , 2 ≤ x ≤ 4
(e) f (x) 2x 3 3x 2 12x, 2 ≤ x ≤ 2
(f) f (x) x 4 18x 2 , 4 ≤ x ≤ 4
15. After a football is punted, its height, h, in metres above the ground at
t seconds can be modelled by h(t) 4.9t 2 21t 0.45.
(a) Determine the restricted domain of this model.
(b) When does the ball reach its maximum height?
(c) What is the ball’s maximum height?
16. Determine the equation of the line tangent to f (x) 4x 3 12x 2 96x
with the smallest slope on the interval 4 ≤ x ≤ 2.
4.3 The First Derivative Test
17. Graph y f ′(x) for the given function.
10
8
6
4
2
–4 –3 –2 –1 0
–2
–4
–6
–8
–10
y
1 2 3 4
y = f(x)
x
18. For each function f (x),
i. find the critical numbers
ii. determine where the function increases and decreases
iii. determine whether each critical number is at a maximum, a minimum,
or neither
iv. use all the information to sketch the graph
CHAPTER 4 REVIEW 335