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in todays lesson we are doing local linear approximation so lets just first think about what those words even mean so approximation so were not getting exact answers were getting close to answers and then think about linear what have we been doing all year long that relates to the linear function if you think about tangent lines are linear functions so we are using tangent lines to make approximations of our function foreign as part of our intro to the lesson Im going to look at a concave up and concave down graph so concave up and here we go concave down unit 5 will we will revisit concavity a lot but for now just kind of the basics of what a concave up is and what concave down is okay so now I want you to imagine a tangent line on each of these functions on these graphs so what we are doing is we are going to use a tangent line so if we have the equation of a tangent line we are going to use that to make approximations on the function at certain values so using the tangent line