Question

use the graph to estimate the slope of the tangent line to y=x^n at the given point. verify your answer analytically. (a) y=x^-1/5, (1,1) (b) y=x^-5, (1,1)

Answer 1

analytically
I think that means we will need to find slope of some secant lines

Answer 2

@myininaya yeah, i think so too, but i don't know how

Answer 3

Well you need to take points close to (1,1) on the same curve and find slope

like find the slope between (1,1) and (.001,f(.001))
then choose closer values than .001

Answer 4

\[\frac{f(.001)-1}{.001-1}\]
this will give you the slope of the secant line that goes through (1,1) and (.001,f(.001))