f(x)=2x^2 - 3x + 1 has a maximum. true false

Explanation:

Step1: Identify the type of function

The function $f(x)=2x^{2}-3x + 1$ is a quadratic function in the form $y = ax^{2}+bx + c$, where $a = 2$, $b=-3$, $c = 1$.

Step2: Analyze the sign of $a$

For a quadratic function $y=ax^{2}+bx + c$, if $a>0$, the parabola opens upward; if $a < 0$, the parabola opens downward. Here $a = 2>0$, so the parabola opens upward.

Step3: Determine existence of maximum

A parabola that opens upward has a minimum value and no maximum value.

Answer:

False