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

-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