Ms. Battaglia AB Calculus

The inverse function of the natural logarithmic function f(x)=lnx is called the natural exponential function and is denoted by f -1 (x) = e x That is, y = e x if and only if x = lny Inverse Relationship ln(e x ) = x and e lnx = x

Solve 9 – 2e x = 7

Solve ln(x – 3) = 2

Let a and b be any real numbers

1. The domain of f(x)=e x is (-∞, ∞), and the range is (0, ∞) 1. The function f(x)=e x is continuous, and one-to-one on its entire domain. 2. The graph of f(x)=e x is concave upward on its entire domain. 3. and

Let u be a differentiable function of x

a.b.

Find the relative extrema and the points of inflection (if any exist) of the function. Use a calculator to confirm your results.

Let u be a differentiable function of x. 1.2.

Find

a.b.

a. b. c.

 AB: Page 360 # odd (skip 113, 115)