4) f (x) = x°+6x+9x+3 Clossify whetn + these antical (D.) Find the points of inflechon If there are any: (€) Find the x and (F) Summanize the points In a table. inclhde add itionod points necessany for the graph ard Sketch the polyndmial uve's in graphing papers. y- intercepts If there are any:
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- The base of a triangle passes through a fixed point (f,g) and its sides are bisected respectively at right angles by the lines y2-8xy-9x2. Find the locus of its vertex.Find b and c so that y=−6x2+bx+c has vertex (−5,−8).Use the method of Lagrange multipliers to find the points on the circle x2 + y2 = 52 that are closest to and farthest from the point (−3, 2).
- When a vertex Q is connected by an edge to a vertesx K, what is the term for the relationship between Q and K A. Q and K are "isolated" B. Q and K are adjacent C. Q and K are "insecure" D. Q and K are "incident"a. Tangents are drawn from any point on the line x + 4a = 0 to the parabola y2 = 4ax. Then find the angle subtended by the chord of contact at the vertex. b.if the chord of contact of tangents from a point P to the parabola y2 = 4ax touches the parabola x2 = 4by, then find the locus of P.Suppose that a temperature of a metal plate is given by T(x,y)=x2+2x+y2, for points (x,y) on the elliptic plate defined by 6x2+5y2≤60. Find the maximum and minimum temperatures on the plate. Use Lagrange Multipliers to determine the absolute extrema of f on the indicated constraint.
- 7. 1. Pick a point where that is not on any of the lines: 2. find the equation of a quadratic function with the chosen point as the vertex. X=0 Y=0 Y=x Y=-xSketch the region that corresponds to the given inequalities. 2x + 4y ≥ 4 2x − 4y ≤ 4 x ≥ 0 The x y-coordinate plane is given. There are 3 lines and a region labeled "solution set" on the graph. The first line enters the window in the second quadrant, goes down and right, passes through the point (−4, 3), crosses the y-axis at y = 1 crossing the vertical line, crosses the x-axis at x = 2 crossing the second line, passes through the point (4, −1), and exits the window in the fourth quadrant. The second line enters the window in the third quadrant, goes up and right, passes through the point (−4, −3), crosses the y-axis at y = −1 crossing the vertical line, crosses the x-axis at x = 2 crossing the first line, passes through the point (4, 1), and exits the window in the first quadrant. The vertical line crosses the x-axis at the origin. The solution set is below the first line, below the second line, and to the right of the vertical line. The regions…Use Lagrange multipliers to find the shortest distance from the given point to the following plane. (5, 4, −4); x + y − z = 1