Explain why hould glvs a eascnabls appraimatonoxwhan h is smal 7h ghes the Ine t

Question

Explain why hould glvs a eascnabls appraimatonoxwhan h is smal 7h ghes the Ine tomulh skpe ohecan lincthat gecs romx-hbox+h It liit a h gcs 1o0 iz alsofix. So for asmall h, this wold be a rosb ppraximaton ofix ' des te slope or the secant line th go“ mom x to x +n its ltit as h gD 10 ls rpg lhe tommula h)-ix) C C. The formula-.h gives te slope ofthe tangent lne tat gocz from x to x + h. Its limit h goes to 0 i2T'XL The formul ghves the . slope oite tangent lme thgoes from x-h to h. Its Imkas h goes to 0 so? (xi 5c for y 5 al h this would be reasonable approrn on off h sint ashg “toDarp: Th.tumia h)-ma Isa or si pe otto socantine thatgoes tonn-xtox.nitsintas poes to

Explanation / Answer

The f(x+h) -f(x) / h is not the slope of tangent line
cuz the limit h --> 0 aint there

So, tat is just the slope of secant line

So, its between options A or D

Look at option D
It says that its the slope of the secant line from -x to x + h
which aint true. It is actually the slope of secant from x to x+ h

So, option A is correct!

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