The function .

(a)

Graph the function .

Draw tangent lines to , at the given values.

is the slope of the tangent line to the and estimate the slope  at the given points from the graph.

Observe the graph,

,, and .

(b)

By the symmetry, slopes of the tangent lines on the left side is also having same magnitude and but going downwards.

So need to do only change the sign.

(c)

  ,, and .

Based on the results of (a) and (b), it seems to be the formula for .

(d)

Derivative of a function is defined as .

The derivative of the given function.

.  

(a) ,, and ..

(b) , and . (c) .