11expx

11expx denotes the function f(x) = 11 e^x, where e is the base of natural logarithms (approximately 2.71828) and the factor 11 scales the standard exponential function vertically. This notation is commonly used to indicate a scaled version of the natural exponential.

The function is defined for all real x and takes only positive values. It has a y-intercept at (0, 11). As x → −∞, f(x) → 0+; as x → ∞, f(x) → ∞. The graph is strictly increasing and convex, reflecting the rapid growth characteristic of exponential functions.

Calculus properties include f'(x) = 11 e^x = f(x), and f''(x) = 11 e^x > 0, confirming its increasing and convex nature. An antiderivative is ∫ f(x) dx = 11 e^x + C. The inverse function is f^{-1}(y) = ln(y/11) for y > 0, since y = 11 e^x implies x = ln(y/11).

In modeling, 11 e^x represents exponential growth with an initial value of 11 at x = 0 and a growth rate governed by the base e. It appears in contexts such as compound interest, population dynamics, and processes scaled by a fixed factor of 11. Related notation includes 11 exp(x), which denotes the same function. It is important to distinguish this from expressions like e^(11x), which have different growth behavior.