Question

Find the equation of the tangent line to the function f(x) = x³ at x = 5.

Answer 1

To find the equation of the tangent line to the function f(x) = x³ at x = 5, find the derivative of the function and evaluate it at x = 5. The equation of the tangent line is y - 125 = 75(x - 5).

Step-by-step explanation:

To find the equation of the tangent line to the function f(x) = x³ at x = 5, we need to find the derivative of the function and evaluate it at x = 5. The derivative of f(x) = x³ is f'(x) = 3x². Evaluating f'(x) at x = 5, we get f'(5) = 3(5)² = 75. Therefore, the equation of the tangent line is y - f(5) = f'(5)(x - 5), which simplifies to y - 125 = 75(x - 5).