Final answer:
The slope of the function f(x)=e^(x)(4x+1) at μ{x}=1 is calculated by taking the derivative of the function and evaluating it at x=1, which results in a slope of 9e^5.
Step-by-step explanation:
The slope of a function at a given point can be found by taking the derivative of the function and evaluating it at that point. In this case, we have the function f(x) = e^((x)(4x+1)) and we want to find the slope at x = 1.
To find the derivative, we can use the product rule and the chain rule. The derivative of e^(u) is e^(u)*(u').
Applying these rules, we get f'(x) = e^((x)(4x+1))*(1+4x+4x^2). Evaluating this at x = 1, we get f'(1) = e^((1)(4*1+1))*(1+4*1+4*1^2) = e^5*(1+4+4) = 9e^5.
Therefore, the slope of the function at x = 1 is 9e^5.