Question

Please help I’m so confused!!!

Answer 1

See below

Explanation:

Obviously, as h ==> 0 it becomes very small

I would pick a very small number for h ..... say -.001

then the equation becomes

[ f (-1.001) - f(-1) ] / (-.001) where f(x) = x^5

= [ (-1.001)^5 - (-1)^5 ] / ( -.001) For the point that has x = -1

= 5.01 <==== approximation for the slope at x = - 1

Now we need line with slope = 5.01 and point (-1,-1)

Using point slope form :

y - -1 = 5.01 (x - -1) re-arrange to:

y = 5.01x - 4.01 <==equation of line with slope = 5.01 and tangent at (-1,-1)

Here is a graph: (and it looks like a good approximation !)