2. DERIVATIVES: 2.1 Tangent Lines and Their Slopes
Remark
Curves have tangent lines only at points where they are smooth.
,2. DERIVATIVES: 2.1 Tangent Lines and Their Slopes
Remark
Curves have tangent lines only at points where they are smooth.
Definition
The slope of a curve C at a point P is the slope of the tangent line to C at P if such a
tangent line exists. In particular, the slope of the graph of y = f (x) at the point x0 is
f (x0 + h) − f (x0 )
lim .
h→0 h
,2. DERIVATIVES: 2.1 Tangent Lines and Their Slopes
Remark
Curves have tangent lines only at points where they are smooth.
Definition
The slope of a curve C at a point P is the slope of the tangent line to C at P if such a
tangent line exists. In particular, the slope of the graph of y = f (x) at the point x0 is
f (x0 + h) − f (x0 )
lim .
h→0 h
Example
x
Find the slope of the curve at the point x = −2.
3x + 2
, 2. DERIVATIVES: 2.1 Tangent Lines and Their Slopes
Normals
Remark
Curves have tangent lines only at points where they are smooth.
,2. DERIVATIVES: 2.1 Tangent Lines and Their Slopes
Remark
Curves have tangent lines only at points where they are smooth.
Definition
The slope of a curve C at a point P is the slope of the tangent line to C at P if such a
tangent line exists. In particular, the slope of the graph of y = f (x) at the point x0 is
f (x0 + h) − f (x0 )
lim .
h→0 h
,2. DERIVATIVES: 2.1 Tangent Lines and Their Slopes
Remark
Curves have tangent lines only at points where they are smooth.
Definition
The slope of a curve C at a point P is the slope of the tangent line to C at P if such a
tangent line exists. In particular, the slope of the graph of y = f (x) at the point x0 is
f (x0 + h) − f (x0 )
lim .
h→0 h
Example
x
Find the slope of the curve at the point x = −2.
3x + 2
, 2. DERIVATIVES: 2.1 Tangent Lines and Their Slopes
Normals
