The graph of the function f(x) = 1 – x² is the upper half of the unit circle. On that curve (see the figure below) we have marked a point P(x, y). normal P(x, y) tangent (-1, 0) (1, 0) (a) What is the slope of the normal at P? Express your an- swer in terms of x and y. (b) Deduce from (a) the slope of the tangent at P. Express your answer in terms of x and y. (c) Confirm your answer in (b) by calculating V1 – (x + h)? – VI – x² | f'(x) = lim h→0 h HINT: First rationalize the numerator of the difference quo- tient by multiplying both numerator and denominator by V1– (x + h)? + VI– x². |

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