# Identify Critical Points

Identifying critical points is paramount in various fields, from engineering and mathematics to business strategy and decision-making. These points signify moments of significance or change within a system or process, often dictating outcomes or indicating areas that require attention. Precision in recognizing these junctures can lead to optimized performance, risk mitigation, and strategic advantages. Whether pinpointing critical points in a mathematical function, identifying pivotal moments in a project timeline, or discerning key market trends, the ability to identify critical points is foundational to effective problem-solving and decision-making across disciplines.

Questions

- Tangents are drawn from the points on the line #x-y+3=0# to parabola #y^2 =8x#. The the variable chords of contact pass through a fixed point whose co-ordinates are?
- How do you find the focus, directrix and sketch #y=x^2-2x#?
- How do you find the coordinates of the center, foci, lengths of the major and minor axes given #y^2/18+x^2/9=1#?
- How do you find the equation of a circle that passes through points (-8,-2)(1-,-11) and (-5,9)?
- How do you identify the vertices, foci, and direction of #(x-3)^2/4-(y+1)^2/9=1#?
- Which of the following is the x coordinates of a stationary point g(x)=9x^2-36x+35 ? answers A, -5/3 B, 5/3 C, 2 D, 7/3 E, 4
- How do I find all the critical points of #f(x)=x^2+4x-2#?
- How do you find the equation of a circle with center on the line x + 2y= 4 passes through the points A(6,9) and B(12,-9)?
- How do you find the center and radius of the circle #x^2-8x+y^2-12y= -51#?
- How do you find the equation of a circle center at the origin; passes through (10, 10)?
- How do you find the center and radius of the circle #(x+4)^2+y^2=49#?
- How do you identify the vertex, focus, directrix and the length of the latus rectum and graph #y=x^2-12x+20#?
- How do you find the foci and sketch the hyperbola #x^2/9-y^2/4=1#?
- How do you write the equation of the circle in standard form, identify the center and radius of #x^2+y^2-2x+6y+9=0#?
- How can I tell whether a parabola opens upward or downward?
- How do you find the center and radius of the circle #(3x-1)^2 + (3y+3)^2 = -1#?
- What are the equations of the tangents drawn from the point (0,1) to the circle #x^2+y^2-2x+4y=0#?
- Please solve q 12 ?
- How do you find the center and radius of the circle #x^2 + y^2 – 8x – 6y – 75 = 0#?
- How do you find the coordinates of the vertices and foci and the equations of the asymptotes for the hyperbola #(y+6)^2/20-(x-1)^2/25=1#?