Use a graphing utility to find the derivative of the function at the given point

Question

(a) Use a graphing utility to find the derivative of the function at the given point, (b) find an equation of the tangent line to the graph of the function at the given point, and (c) Use the utility to graph the function and its tangent line in the same viewing window.

g (t) = 3t2/√(t2 + 2t -1), (1/2, 3/2)

Answer 1

Step 1:

a)

The function is  and the point is  .

 Graph:

Graph for the function and its derivative.

The derivative of the function at is -3.

Step 2:

b)

The function is  and the point is  .

Apply derivative on both sides.

    

Since  and

 

Multiply and divide both numerator and denominator with .

Find the derivative at the point .

Substitute in

.

Slope of the tangent line -3.

Answer 2

Step 3:

Find the tangent line equation using the formula 

Multiply both sides by 2.

.

The tangent line equation is .

Step 4:

c)

Graph:

Graph the function and tangent line.

Solution:

a)

b) The tangent line equation is

c)