Function Analysis of Function Analysis of Exponential, Exponential,

Logarithmic & Logarithmic & Trigonometric FunctionsTrigonometric Functions

Calculus - SantowskiCalculus - Santowski

Review Determine the equation of dy/dx

if:

y = 2x y = ex

y = log5x y = ln(x)

y = sin(x) y = cos(x)

Function Analysis 1. Find the absolute minimum of

on the interval (0,∞)

2. Find the intervals of increase/decrease of f(x) = ex + e-

2x

3. Find the intervals of increase/decrease for the function f(x) = x2e-x

€

y =ex

x

Function Analysis

1. Find the minimum point of the function

2. Find the max pt of

3. Find where y = ln(x2 – 1) is increasing and decreasing

4. Find the maximum value of

04/20/23 Calculus - Santowski 4

€

f (x) = x − ln x

€

g(x) = ln x − ex−1

€

h(x) =ln x

x

Function Analysis Find the maximum and minimum

point(s) of the function f(x) = 2cosx + x on the interval (-π,π)

Find the minimum and maximum point(s) of the function f(x) = xsinx + cosx on the interval (-π/4,π)

Find the interval in which g(x) = sin(x) + cos(x) is increasing on xER

04/20/23 Calculus - Santowski 5