f(x)=3x^2-90x+177 The given equation defines the function f.For what value of ac does f(x) reach its minimum? square

To find the value of \( x \) at which the function \( f(x) = 3x^2 - 90x + 177 \) reaches its minimum, we need to determine the vertex of the parabola. The vertex form of a quadratic function \( ax^2 + bx + c \) is given by:<br /><br />\[ x = -\frac{b}{2a} \]<br /><br />For the given function \( f(x) = 3x^2 - 90x + 177 \):<br /><br />- \( a = 3 \)<br />- \( b = -90 \)<br /><br />Substitute these values into the formula:<br /><br />\[ x = -\frac{-90}{2 \cdot 3} = \frac{90}{6} = 15 \]<br /><br />Therefore, the function \( f(x) \) reaches its minimum value when \( x = 15 \).<br /><br />So, the value of \( x \) at which \( f(x) \) reaches its minimum is \( \boxed{15} \).