Final answer:
To find the equation of the tangent line to the graph of f(x) = -x³ at (-1,1), first calculate the derivative to get the slope of -3, then use the point-slope form to get the equation y = -3x - 2.
Step-by-step explanation:
The question involves finding the equation of a tangent line to a cubic function at a given point. To find this equation, first calculate the derivative of the function to find the slope of the tangent line. The derivative of f(x) = -x³ is f'(x) = -3x². Evaluating the derivative at the point x = -1, we get f'(-1) = -3(-1)² = -3, which is the slope of the tangent line at (-1,1).
Next, to find the tangent line's equation, use the point-slope form y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point of tangency. Substituting the values, we get y - 1 = -3(x + 1). Simplifying, y = -3x - 3 + 1, and finally, y = -3x - 2.
This tangent line has a slope of -3 and a y-intercept of -2, which are represented by the terms m and b in the linear equation y = mx + b.