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)

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anonymous · Answer

attachment

myininaya · Answer

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

anonymous · Answer

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

myininaya · Answer

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

myininaya · Answer

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