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Find the location and nature of the turning point of the line y=-x^2+3x+2

Location is placed where the gradient is 0.Differentiate the line to get dy/dx = -2x + 3 and set it equal to zero.2x = 3 therefore x = 1.5.Plug back into the line equation to find the coordinate. y = -(1.5)2 + 3(1.5) +2 = 4.25. Nature of turning point is determined by the second derivative. d2y/dx2 = -2. -2 < 0 therefore turning point is a maxima.
Final answer : location is (1.5,4.25) and it is a maxima.

ER

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