Section 5.4

Exponential Functions –Differentiation and Integration

The inverse of the natural log function is 𝑓 𝑥 = 𝑒𝑥

-3 -2 -1 1 2 3

-3

-2

-1

1

2

x

y

Ex1: Solve 17 xe

Ex2: Find the relative extrema of ( ) xf x xe

Ex3: Integrate

a) b)3 1xe dx

2

5 xxe dx

c) d)

1

2

xedx

xcos(sin )( )xx e dx

Ex4a: 1

0

xe dx

1

1

x

y

Ex4b: 1

01

x

x

edx

e

1

1

x

y

Ex4c: 0

1

cos( )x xe e dx

-1

1

x

y