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1 March, 01:07

Consider the function f defined by f (x) = (1 - x) (5 - 2x)

What is the minimum value of f (x) ?

-

9/8

-9/8

7/4

-5

+5
Answers (1)
  1. 1 March, 02:39
    0
    -9/8

    Step-by-step explanation:

    The minimum value of f (x) is at f' (x) = 0

    Given;

    f (x) = (1-x) (5-2x)

    Expanding f (x), we have;

    f (x) = (5 - 5x-2x + 2x^2)

    f (x) = 5 - 7x + 2x^2

    Differentiating f (x);

    f' (x) = - 7 + 4x

    At f' (x) = 0

    f' (x) = - 7 + 4x = 0

    4x = 7

    x = 7/4

    f (x) is minimum at x = 7/4

    Substituting into the function f (x);

    f (7/4) = (1-x) (5-2x) = (1 - 7/4) (5 - 2 (7/4))

    f (7/4) = (-3/4) (6/4) = - 18/16

    f (7/4) = - 9/8

    f (x) is minimum at f (7/4) = - 9/8
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