Name: Date: Period: Assignment1D:RatesofChange Lippman/Rasmuss smussen explanation,, Answer the following problems from your Lippman/Ra smuss en textbook with as much detail, explanation and work that is appropriate. 1.3: 1.3: 10, 12, 20, 38 Find the average rate of change of each function on the interval specified. t 2 − 4t + 1 on [-3, 1] t2 + 3 The inputs = − and = when put into the function () produce the points ((-3, ) and 10. p (t ) = ି ି (1,− (1, ). The average rate of change between these two points is ି(ି) = ି ି ା = ି =− ∗ ૠ = − = − . Find the average rate of change of each function on the interval specified. Your answers will be expressions involving a parameter (b or h). 12. g ( x) = 2 x 2 − 9 on [4, b] The inputs = and = when put into the function () produce the points (4,23) (4,23) and (, − ૢ).. : () = () − ૢ = () − ૢ = − ૢ = , () = () − ૢ. The average rate of change between these two points is ൫ ି൯ ି = (ା)(ି) (ି) ൫ ିૢ൯ି ି = ିૢି ି = ି ି = = ( + ). 20. g ( x) = 3x 2 − 2 on [x, x+h] The inputs = and = + when put into the function () produce the points (, ( − )) and ( + , ( + ) − ).. The average rate of change between these two points is ൫(ା) ି൯ି൫ ି൯ (ା)ି ାା ି = = ൫(ା) ି൯ି൫ ି൯ ା = (ା) ି ି ା = + = ( + ). Problems from: Precalculus: An Investigation of Functions; Lippman & Rasmussen. 2014. = (ା) ି = ൫ ାା ൯ି = Use a graph to estimate the local extrema and inflection points of each function, and to estimate the intervals on which the function is increasing, decreasing, concave up, and concave down. 38. h( x) = x 5 + 5 x 4 + 10 x 3 + 10 x 2 − 1 From the graph, we can see that the function is decreasing on the interval (−, ),, and increasing on the intervals (−∞, −)( ܌ܖ܉, ∞).. This means that the function has a local minimum at = , = ܜ܉ ܕܝܕܑܠ܉ܕ ܔ܉܋ܗܔ ܉ ܌ܖ܉−. We can estimate that the function is concave down on the interval (−∞, −),, and concave up on the intervals (−∞, −)( ܌ܖ܉, ∞). This means there is an inflection point at = −.

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