Answer:
-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
