# the slope of the secant line and tangent line...

For the function g(x) whose graph is shown, give the value of each quantity, if it exists. If it does not exist, explain why.

a) The slope of the secant line between the points with x coordinates 3 and 4.

b) The slope of the tangent line to the graph at the point with the x coordinate 6

(c) g(0)

(d) lim x→2 g(x)

(e) lim x→3+ g(x)

asked Jan 27, 2015 in CALCULUS

(a)

Step 1:

Observe the graph :

As- coordinate approaches- coordinate tends to .

As- coordinate approaches- coordinate tends to .

The slope of the secant line using the two pints is .

Substitute and in the slope equation.

Slope of the secant line is .

Solution:

Slope of the secant line is .

(b)

Step 1:

Observe the graph :

As- coordinate approaches , - coordinate tends to .

Consider another point from a graph with small change in.

As- coordinate approaches , - coordinate tends to .

The slope of the tangent line using basic derivative form is

Substitute and   in the slope equation.

Slope of the tangent line is .

The graph has horizontal tangent line at .

Solution:

Slope of the tangent line is .

(c)

Step 1:

Observe the graph :

The hallow circle in the graph indicates that , the point is not included in its domain.

is not included in the domain of .

Therefore does not exist .

Solution:

does not exist.

(d)

Step 1:

Observe the graph :

We can observe from the graph that  exists.

As approaches to  from the left side then approaches to approximately.

As approaches to from the right side then approaches to approximately.

Since the left hand limit and right hand limit are equal, Limit exist.

Solution:

.

(e)

Step 1:

Observe the graph :

As approaches to from the right side then approaches to approximately.

Solution:

.