Final answer:
To find the points on the curve x²/9 + y²/16 = 1 where the tangents are parallel to the x-axis and y-axis, we can differentiate the equation and find the points that satisfy the respective conditions.
Step-by-step explanation:
To find points on the curve x²/9 + y²/16 = 1 where the tangents are parallel to the x-axis, we can consider the equation of the curve which is in the form of an ellipse. To find these points, we need to solve the equation when the slope of the tangent is 0. We can differentiate the equation and find the points that satisfy the condition.
Similarly, to find points on the curve where the tangents are parallel to the y-axis, we again consider the equation of the curve as an ellipse. In this case, we need to solve the equation when the slope of the tangent is undefined. By differentiating the equation, we can find the points that satisfy the condition.