Final answer:
The main use of a calculator when finding the equation of a tangent line to a curve is to compute derivatives, which provides the slope necessary to form the equation of the line. c) To compute derivatives is the correct answer.
Step-by-step explanation:
The primary purpose of a calculator when finding the equation of a tangent line to a curve is to compute derivatives. The slope of the tangent line at any given point on the curve is equal to the derivative of the curve's equation at that point.
By computing the derivative, you can determine the slope of the tangent line, which is essential in writing its equation. Once you have the slope and a point through which the line passes (the point of tangency), the equation of the tangent line can be written using the point-slope form.
An equation of a line is understood through its slope and intercept, and when we compute a derivative, we are finding the instantaneous rate of change, which for a function's graph, translates to the slope of the tangent line at a certain point.
Calculators do not primarily evaluate integrals, solve differential equations, or graph the curve in this context, but rather assist in the necessary computation of derivatives to establish the line's slope.