he equation dy dx (r,0) econd derivative is r = 60, = f'(0) sin 0 + f(0) cos 0 f'(0) cos 0 -f(0) sin 0 dy dy'/de 2 dx² dx/d0 = I 0=2, 2π gives a formula for the derivative y' of a polar curve r = f(0). The Find the slope and concavity of the following curve at the given points.

Need to find the Horizontal and Vertical Tangent Line of r=3-2 cos theta. I know I need to set the each equation to zero but I am having difficulty breaking down the trig functions. For dy: 2 sin^2 theta+4 cos theta = 0 for dx : 2 sin theta cos theta-4 sin theta = 0

Question 4 Consider the curve 5x2+4xy+4y3 = 29125 (a) Show that P(-75,-5) is on the curve i.e., show that P satisfies 5x² + 4xy + 4y³ (b) Find dy dx i.e., y'. (c) Determine the value of y' at P by.... (i) using the expression in (b), and = 29125. (ii) substituting the coordinates of the point immediately after you carry out the differen- dy tiation in (b) (i.e, right before you start solving for the d) dx What do you observe? (d) A portion of the curve of 5x² + 4xy+4y³ 29125 is illustrated below. A D B E Which of the labelled points could be P(-75, -5)? Briefly justify your answer.

2 a) FIND dy BY IMPLICIT DIFFERENTIATION: x4y3 = -8 dx b) EVALUATE THE DERIVATIVE FROM PART a AT THE POINT (1, -2). 3. FIND THE SLOPE OF THE TANGENT LINE TO THE GRAPH OF 5x + 2xy + 4y² = 25 AT THE POINT (1,2).