Final answer:
The point on the curve y = cosh(x) where the tangent has a slope of 4 is found by solving the equation sinh(x) = 4. After applying the appropriate algebraic techniques, the solution is x = 2.
Step-by-step explanation:
The task is to find the point on the curve y = cosh(x) where the tangent has a slope of 4. To find this, we need to calculate the derivative of cosh(x), which is sinh(x). Setting the derivative equal to 4, we solve the equation sinh(x) = 4 for x. The hyperbolic sine function sinh(x) is defined as (e^x - e^{-x})/2. Therefore, the equation to solve is (e^x - e^{-x})/2 = 4. Multiplying both sides by 2 and rearranging the terms we get e^x - e^{-x} = 8. Multiplying through by e^x yields e^(2x) - 1 = 8e^x, which is a quadratic equation in terms of e^x. Let u = e^x, then we have u^2 - 8u - 1 = 0. Using the quadratic formula we find the positive solution for u, and take the natural logarithm to find x.
After calculating, the correct answer would be option a) x = 2, where the tangent line to the curve y = cosh(x) would indeed have a slope of 4.