Final answer:
To find the point where the tangent to the curve y = cosh(x) has a slope of 5, calculate the derivative of cosh(x), which is sinh(x), and solve for x when sinh(x) = 5. Use the inverse hyperbolic sine function to find x, and substitute back into the original equation to find the corresponding y value.
Step-by-step explanation:
To find the point on the curve y = cosh(x) where the tangent has a slope of 5, we need to find the derivative of cosh(x) and then solve for x when the derivative is equal to 5.
The derivative of cosh(x) is sinh(x), so we set sinh(x) = 5 and solve for x. The inverse hyperbolic sine function, arsinh() or sinh-1(), is used to find x, which yields x = sinh-1(5).
Once we have the value of x, we can find the corresponding y value by substituting x back into the original equation y = cosh(x).