Final answer:
The slope of the tangent line to the graph of y = -43x² + 3x - 2 at (3, 1/4) is -255. The equation of the tangent line is y - 1/4 = -255(x - 3).
Step-by-step explanation:
To find the slope of the tangent line to the graph of y = -43x² + 3x - 2 at the point (3, 1/4), we need to find the derivative of the function and evaluate it at x = 3.
The derivative of y = -43x² + 3x - 2 is dy/dx = -86x + 3.
Evaluating this derivative at x = 3, we get dy/dx = -86(3) + 3 = -255.
Therefore, the slope of the tangent line to the graph of y = -43x² + 3x - 2 at the point (3, 1/4) is -255.
The equation of a tangent line is given by y - y1 = m(x - x1), where m is the slope of the tangent line and (x1, y1) is a point on the line.
Substituting the values we have, the equation of the tangent line is y - 1/4 = -255(x - 3).