PARTICIPATION ACTIVITY ust Find the equation of the line tangent to the graph of \( f(x)=3 x^{2}-7 \) at \( x=2 \). Use the point-slope form. Inducte a multialication sign between symbols. For example, \( a * x \).

To find the equation of the tangent line to the function \( f(x) = 3 * x^{2} - 7 \) at \( x = 2 \), we first need to calculate the slope of the tangent line, which is represented by the derivative \( f'(x) \). The derivative of \( f(x) \) is \( f'(x) = 6 * x \). Evaluating this at \( x = 2 \) gives us \( f'(2) = 6 * 2 = 12 \). Now, we also need the point on the graph at \( x = 2 \): \[ f(2) = 3 * (2^2) - 7 = 3 * 4 - 7 = 12 - 7 = 5. \] So the point of tangency is \( (2, 5) \) and the slope is \( 12 \). Using the point-slope form of the line equation \( y - y_1 = m * (x - x_1) \), we have: \[ y - 5 = 12 * (x - 2). \] This is the equation of the tangent line at the given point!