Find the values of \( x \) for which the graph of \( f(x)=3 x^{2}-4 x+2 \) has a tangent line parallel to the line \( y=5 x+4 \) Enter the exact answers. The field below accepts a list of numbers or formulas separated by semicolons (e.g. \( 2 ; 4 ; 6 \) o \( x+1 ; x-1 \) ). The order of the list does not matter. \( x=1 \)

To find the values of \( x \) for which the tangent line to the graph of \( f(x) = 3x^2 - 4x + 2 \) is parallel to the line \( y = 5x + 4 \), we first need to determine the slope of the tangent line, which is given by the derivative of \( f(x) \). Calculating the derivative: \[ f'(x) = \frac{d}{dx}(3x^2 - 4x + 2) = 6x - 4 \] We set the derivative equal to the slope of the given line: \[ 6x - 4 = 5 \] Solving for \( x \): \[ 6x = 9 \implies x = \frac{9}{6} = \frac{3}{2} \] Thus, the values of \( x \) for which the graph has a tangent line parallel to the line \( y = 5x + 4 \) is: \[ x = \frac{3}{2} \] So, the final answer is: \[ \frac{3}{2} \]