Calculus of a Single Variable, Chapter 2, 2.3, Section 2.3, Problem 66

You need to evaluate the equation of the tangent line at (4,7), using the formula:
f(x) - f(4) = f'(4)(x - 4)
Notice that f(4) = 7.
You need to evaluate f'(x), using the quotient rule, such that:
f'(x) =((x+3)'(x - 3) - (x + 3)(x - 3)')/((x - 3)^2)
f'(x) = (x - 3 - x - 3)/((x - 3)^2)
f'(x) = -6/((x - 3)^2)
You need to evaluate the derivative at x = 4:
f'(4) = -6/((4-3)^2) =>< f'(4) = -6
Replacing the values into equation yields:
f(x) - 7= -6(x - 4)
f'(x) = -6x + 31
Hence, evaluating the equation of the tangent line at the given curve, yields f'(x) = -6x + 31.