1. Consider the implicity function 2 x = y - x^2/ x + 2y

a) Verify that the points A(l,-1) and B(-2,4 lie on the graph of this equation. b) In part of this worksheet you will be asked to verify the derivative formula Lt by implicitly differentiating the equation given above. Evaluate this derivative at points A and B C) y= x^3/(1-4 x) The derivative for y = -12x^2+6x/ (1- 4x)^2

Those things I aleardy have it I need the solve for these part under this sentence ( f, g,h, i, and j )there are five questions ,and please please write which letter is related to know exactly the answer

F) Using the explicit derivative formula f(x) obtained in part c . find all points on the graph of y =:f (x) where the tangen line is horizontal . Then substitute the x and y-coordinates of . each point into the implicit derivative dy/dx formula given in part(b ) to confirm the slope value .

G) Again using the explicit derivative formula from part(c), find all points on the of f where the tangent slope equals 6.Now substitute the x- and y coordinates of where the graph each such point into the implicit dy formula given in part(b) to confirm this slope value.

H ) It is clear that no point(x,y) for which x +2 y= 0 will appear on the graph of the implicit equation 2x= y - x^2/ x+2y . In effect, points on the line x +2y =0 are"cut out" of the graph r of the explicit function f . Relate this observation to the phenomenon encountered earlier part ( e ) and ( f) .

i) once again referring to the explicit function f (x) obtained in part (c) ,where does the graph of f have a vertical asymptotes? What happens when you substitute this x-value into the original implicit equation and attempt to solve for y ? Explain.

j) ( verification of the implicit derivative given in part (b).implicitly differentiate the orginal equation, applying the quotient rule on the right-hand side ,clear the denominator and expand terms , then solve for dy/dx and simplify. ?

( please I need all the answers for five questions and write the letter on front each part)