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Given the function f (x) = (x ^ 2-4x + a) / x, 1 is less than or equal to x, less than or equal to 5, a belongs to R. if a = 4, find the maximum value of function f (x). If 1 is less than or equal to x, less than or equal to 5, the inequality f (x)
1. Take a = 4, f (x) = x-4 + 4 / x, then f ′ (x) = 1-4 / X2, Let f ′ (x) = 0, get two solutions x = 2, X ′ = - 2
Then f (2) = 0, f (- 2) = 8, f (1) = 1, f (5) = 1.8
2. If f (x) < 0 is constant, only the maximum value is less than zero
F (2x-1) = x ^ 2 + 4x to find f (x)
Let y = 2x-1, then x = (y + 1) / 2, and substitute f (2x-1) = x ^ 2 + 4x
f(y) = (y+1)^2/4 + 4 * (y+1) / 2
= (y^2+2y+1) / 4 + 2y + 2
= y^2/4 + 5y/2 + 9/4
therefore
f(x) = x^2/4 + 5x/2 + 9/4
F (2x-1) = 4x ^ 2 + 5x for f (x)~
Thanks for the process
Analysis
Let 2x-1 = t
x=1/2(t+1)
therefore
f(t)=(t+1)²+5(t+1)/2
=t²+2t+1+5t/2+5/2
=t²+9t/2+7/2
T x interchange
f(x)=x²+9x/2+7/2
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