MATH 1007 Lecture Notes - Lecture 8: Minimax, Maxima And Minima

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6 Apr 2016

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A funcion f has an absolute maximum (or global maximum) at c if f(c) is greater or equal to f(x) for all x in the domain of f. The number f(c) is called the maximum value of f on d. Basically, a max is the f(x) value higher than all the others. A funcion f has an absolute minimum (or global minimum) at c if f(c) is smaller or equal to f(x) for all x in the domain of f. The number f(c) is called the minimum value of f on d. Basically, a min is the f(x) value lower than all the others. The maximum & minimum values of f are called the extrema or extreme values of f. A funcion f has a relaive maximum (or local maximum) at c if f(c) to f(x) when x is near c.

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blushdinosaur923

Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum values of f.?

f(x) = {36 â x^2 if â6 â¤ x < 0

{3x â 3 if 0 â¤ x â¤ 6

It is a piecewise function.

Find abs max/min, local max/min. (If an answer does not exist, enter DNE.)

Thanks!

Find the derivative of the function and evaluate thederivative at the given x-value.

f(x) = 2x² at x = 1

A) f' (x) = 4x; f' (1) = 2
B) f ' (x) = 2x; f ' (1) = 2
C) f' (x) = 4x²; f' (1) = 4
D) f' (x) = 4x; f' (1) = 4

f(x) = 6x + 2; [-1, 2]

A) Absolute maximum: 12, absolute minimum: -6
B) Absolute maximum: -1, absolute minimum: 2
C) There are no absolute extrema.
D) Absolute maximum: 14, absolute minimum: -4

f(x) = (-5x + 7)⁴

A) f '(x) = -5(-5x + 7)³
B) f '(x) = -20(-5x + 7)⁴
C) f '(x) = 4(-5x + 7)³
D) f '(x) = -20(-5x + 7)³

A)
B)
C)
D)

A company estimates that the daily revenue (in dollars) from thesale of x cookies is given by

R(x) = 885 + 0.02x + 0.0003x²

Currently, the company sells 900 cookies perday.

Use marginal revenue to estimate the increase in revenueif the company increases sales by one cookie per day.

A) $92.00
B) $0.56
C) $56.00
D) $0.92

f(x) = -3 - 7x; [-3, 1]

A) Absolute maximum: -10, absolute minimum: -24
B) Absolute maximum: 18, absolute minimum: -10
C) There are no absolute extrema
D) Absolute maximum: 24, absolute minimum: -4

A)
B)
C)
D)

s(x) = -x² - 20x - 19

A) Relative maximum at ( -20, -19)
B) Relative maximum at ( 10, 81)
C) Relative maximum at ( -10, 81)
D) Relative minimum at ( 20, -19)

Differentiate.

f(x) = (5x + 4)²

A) f'(x) = 10(5x + 4)²
B) f'(x) = 5(5x + 4)
C) f'(x) = 2(5x + 4)
D) f'(x) = 10(5x + 4)

10.

Find the absolute maximum and absolute minimum values ofthe function, if they exist, over the indicated interval. When nointerval is specified, use the real line (-?, ?).

f(x) = -21; [ -7, 7]

A) Absolute maximum: 21, absolute minimum: 0
B) Absolute maximum: 21, absolute minimum: -21
C) Absolute maximum: -21, absolute minimum: -21
D) There are no absolute extrema.

11.

A)
B)
C)
D)

12.

f(x) = -6x² - 2x - 7

A) Relative maximum at
B) Relative maximum at
C) Relative maximum at
D) Relative maximum at

13.

f(x) = 0.2x² - 2.4x + 5.9

A) Relative minimum at ( 6, -1.3)
B) Relative maximum at ( 6, -1.3)
C) Relative minimum at ( -6, 27.5)
D) Relative minimum at ( 6, 0)

14.

A grocery store estimates that the weekly profit (in dollars)from the production and sale of x cases of soup is given by