A curve is defined by y=x sqrt(x-1), find dy/dx and the gradient at (5,10)?

X = (y2 - y1)/(x2 - x1) where (x1, y1) = coordinates of the first point (P) (x2, y2) = coordinates of the second point (Q) So for part (i) Q = (7.5,?(7.5 - 7)) Q = (7.5,?.5) Q = (7.5, .707107) Slope = (.707107 - 1)/(7.5 - 8) Slope = -.292893/-.5 Slope = .585786 (b) You should find the slope approaches 1/2 as Q gets closer to P. (c) The tangent line will have the form: y = mx + be where (x, y) = points on the line m = slope.

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