Final answer:
The equation of the tangent to the graph of f(x) = x² - 8 at x = 3 is y = 6x - 17.
Step-by-step explanation:
To find the equation of the tangent to the graph of f(x) = x² - 8 at the point where x = 3, we first need to calculate the derivative of f(x), which will give us the slope of the tangent. The derivative f'(x) of f(x) is 2x. At x = 3, the slope of the tangent is therefore f'(3) = 2· 3 = 6. The value of the function at x = 3 is f(3) = 3² - 8 = 1. Using the point-slope form of a line, y - y1 = m(x - x1), with m = 6 and point (3, 1), we get the equation of the tangent line: y - 1 = 6(x - 3), which simplifies to y = 6x - 17.