Calculus

posted by .

If f(x) has zeros at x=a, and x=b, the x coordinate of the turning point between x= a and x=b is 1/2(a+b).
PLease help i don't understand this!

  • Calculus -

    is it some times true or always true?? that's the question

  • Calculus -

    Turning point is the point at which the slope of the graph changes direction, i.e. from positive to negative or vice versa.

    This happens when dy/dx=0.

    In the case of a quadratic function,
    f(x)=ax²+bx+c,
    dy/dx=2ax+b=0, or this happens when
    x=-b/2a

    It turns ou5 that the real zeroes of the quadratic function are at
    x1,x2=(-b±sqrt(b²-4ac))/2a
    and (x1+x2)/2 = -b/2a.

    So, yes, the "turning point" where the function is a maximum/minimum happens at the average of the two zeroes. However, this is true only for the case of the quadratic equations, and is not generally true for all functions.

  • Calculus -

    but what if its not a quadratic function?.. isn't it possible to have a function that has two zeros but is not a quadratic.. for example the first zero is passed by a cubic kind of curve that is connected to a straight line going to the other zero? so would it be quintic, so does the same thing apply?

    And is the question always true, sometimes true, or never true?

  • Calculus -

    "is not generally true for all functions. "
    means that it is possible that dy/dx=0 at the average of two roots, but in general it is not true.

    Example when it is true:
    sin(x)=0 at x=0 and x=π.
    dsin(x)/dx=0 at x=π/2

    Example when it is not true:
    y=x(x-1)(x-2)=x³-3x²+2x
    y(0)=y(1)=y(2)=0
    dy/dx=0 at x=1±(√3)/3

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. maths(urgent)thanks.

    a parabola with turning point at (1,-2) and passing through the origin.find the equation of this parabola. how do i do this?
  2. college calculus

    a point is moving on the graph of xy=30. when the point is at (6,5), its x-coordinate is increasing by 6 units per second. how fast is the y-coordinate changing at the moment
  3. college calculus

    a point is moving on the graph of xy=30. when the point is at (6,5), its x-coordinate is increasing by 6 units per second. how fast is the y-coordinate changing at the moment
  4. calculus-can someone please help me with this ques

    Given the following polynomial f(x)=(x-1)(x-5), find A.the zeros and the multiplicity of each one b. where the graph crosses or touches the x-axis c.the number of turning points d. the end behavior Please show work.
  5. calculus

    Iamhaving a really hard time trying to understand this question. Can someone please show me how to work this question. Give the following polynomial, find a. the zeros and the multiplicity of each b. where the graph crosses or touches …
  6. calculus-can someone please help me with this ques

    Given the following polynomial find, a. zeros and the multiplicity of each b. number of turning points c. end behavior f(x)=(x-1)(x-5) a. the multiplicity of (x-1)(x-5) x=1 and x=5----is this correct b. number of turning points I had …
  7. calculus--please help!!

    I have two questions that I don't understand and need help with. 1. information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zerosof f. degree 4, zeros i;9+i 2. form a polynomial f(x) with …
  8. Calculus-Applied Optimization Problem:

    Find the point on the line 6x + 3y-3 =0 which is closest to the point (3,1). Note: Your answer should be a point in the xy-plane, and as such will be of the form (x-coordinate,y-coordinate)
  9. maths

    a)Express y = 2 (x - 1) (x - 5) in the form y = ax^2 + bx + c. b) From the above quadratic equation calculate the following: I) x and y intercepts II) Coordinate of the turning point III) Is the graph a maximum or minimum turning point?
  10. Calculus

    A point is moving along the curve xy=12. When the point is at (4,3), the x-coordinate decreases at the rate of 2cm/sec. How fast is the y-coordinate changing at that point?

More Similar Questions