Question

Use a graph to estimate the coordinates of the lowest point and the leftmost point on the curve x = t4 – 35, y = t + 314. Then find the exact coordinates. (x, y) = ( (I) (lowest point) (x, y) = (leftmost point) Need Help? Read It Talk to a Tutor

Answer 1

From the graph we get an approximate leftmost point at about (-1.2, 1.2), lowest point (1.4, -0.5) 35 3 2.5 2 1.5 (-1.19037 1.17007) 0.5 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 -0.5 (1.40237,-0.47241) -1

Solution x=that, y=++344 dy da First find the derivative dy 3 da = 4+² 3 dt = 1+12t dt dy 318 dt da da dt = 1+1243 dt 4+² 3 The vertical tangent would be where da so. This is where we find the leftmost point Let ² 3=0 3 t = 3/4 "3 t= (3₂) t = 0.9 Find the Coordinates. a=((3143)334–3(34) 43 = (3/4) 3 - 2 1/4 4 0.6-2.25 x = -1.65

is where we find the lowest point $31%21'5 y (33-36%)34 0.97370.6) The horizontal tangent would be where dy dt = 0.9+1.8 y = 2,7 =0. This testrzo 1+12+²=0 12+² = -1 +=(-11) +=(-0.083) +='s Find the coordinates 2 353-3()s 3(te 43 X- 43 (7) +3

육 (주) () 24 (GI) () + x