Suppose, f(x) is a function satisfying the following conditions (a) f(0) = 2, f(1) = 1 (b) f has a minimum value at x=52, and (c) for all x, f′(x)=∣∣∣∣2ax2ax−12ax+b+1bb+1−12(ax+b)2ax+2b+12ax+b∣∣∣∣ where a, b are some constants. Determine the constants a, b and the function f(x).

Suppose, f(x) is a function satisfying the following conditions (a) f(

1.	Suppose, f(x) is a function satisfying the following conditions (a) f(0) = 2, f(1) = 1 (b) f has a minimum value at x=52, and (c) for all x, f′(x)=∣∣∣∣2ax2ax−12ax+b+1bb+1−12(ax+b)2ax+2b+12ax+b∣∣∣∣ where a, b are some constants. Determine the constants a, b and the function f(x).
Answer» Suppose, f(x) is a function satisfying the following conditions (a) f(0) = 2, f(1) = 1 (b) f has a minimum value at $x = \frac{5}{2}$ , and (c) for all x, $f^{'} (x) = ∣ ∣∣ ∣ \begin{matrix} 2 a x & 2 a x - 1 & 2 a x + b + 1 b & b + 1 & - 1 2 (a x + b) & 2 a x + 2 b + 1 & 2 a x + b \end{matrix} ∣ ∣∣ ∣$ where a, b are some constants. Determine the constants a, b and the function f(x).