Graphically, find the tangent line to the graph of the function

at the point **(0.5, 0.0625)** as the limit of secant lines.

Using Microcalc:

- Choose
*Beginning Calculus*from the initial menu and press . - Use the arrow keys to move to the menu item
*Secants and Tangents*, press and . - At the prompt
*F(x) =*, enter the formulax^4 - and use the bounds
- x0 = -1.5 x1 = 1.5
- y0 = -1 y1 = 4

- Use the arrow keys to move to
*Key in Base Point*and press . - At the prompt
*a =*, type in 0.5 . - You will then see the point (0.5, 0.0625) on the graph of this function.
- Press and use the arrow keys
to choose
*Choose Positive h*and press and . - You will then see the following:
- (*) Press and
and will see:
Point-slope equation of the secant: y = c(x - a) + b c = 1.500000 a = 0.500000 b = 0.062500, (h = 1.000000)

- Press and use the arrow keys
to move to
*h <<-- h/2*and press twice. - You will now see, superimposed on the previous graph, the secant line from (0.5, 0.0625) to (0.75, 0.3164). As you repeat these steps from (*) above, you will see the secant lines approaching the tangent line.