The point P 4 1 lies on the curve y x 3 a If Q is the point x x 3 use your calculator to find the slope of the secant line PQ correct to six decimal places for the following values of x 1 3 5 0 585786 ii 3 9 iii 3 99 iv 3 999 v 4 5 vi 4 1 vii 4 01 viii 4 001 b Using the results of part a guess the value of the slope of the tangent line to the curve at P 4 1 0 5 c Using the slope from part b find an equation of the tangent line to the curve at P 4 1 y d Sketch the curve two of the secant lines and the tangent line
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