Question

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

Answer 1

-9/8

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