14. Find the orthogonal trajectories of the family of curves 1 y =- (x + k)³ (a) y = (3x+ C)/7 (d) y = (유프 + C)"7 (b) y = (유z+ C)' (e) y = (금x + C)’ (e) y = (3x + C)³/"

Find the maximum point of the curve y=---- -2x+1 2 A. 3 (2-) B. C. D.

8) Find the slope of the graph of y = V2x2 + 1 at the point (2, 3).

The point P(4, -2) lies on the curve y = 2/(3 - x). (a) If Q is the point (x, 2/(3x)), use your calculator to find the slope mpo of the secant line PQ (correct to six decimal places) for the following values of x. (i) 3.9 mpQ = (ii) 3.99 mpQ = (iii) 3.999 mpQ (iv) 3.9999 mpq = E = 4.1 mpQ = (vi) 4.01 mpQ = (viii) (vii) 4.001 mpQ = mpQ = 4.0001 (b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve at P(4, -2). m = (c) Using the slope from part (b), find an equation of the tangent line to the curve at P(4, -2).