Determine the maximum and minimum number of turning points for the function h(x) = -2x^4 - 8x^3 + 5x -6.


Is this a valid reason:

A quartic polynomial function has a 3 Turning points. The turning point is always 1 less than the degree. For example degree 4=3 TP, degree 5=4 turning points?

What about the minimum?

  1. 👍 0
  2. 👎 0
  3. 👁 1,784
  1. If the x^4 term is positive, then the curve rises in the 1st and 2nd quadrants, so there has to be at least one minimum point.
    if the x4 term is negative, then the curve drops down in the 3rd and 4th quadrants, and there has to be at least one maximum.
    For yours the curve will be downwards, so it could look like an upside down W

    Draw a WW. You will see that there are 2 mins and 1 max if it opens up, and if the curve looks like an M, (-x^4), there could be 2 max's and 1 min
    There cannot be 3 max's and 1 min for a quartic

    Your statement about the turning points is correct, but those turning points could be maximums or minimums
    I will give you a few examples of equations where it is obvious, I will leave the equations in factored form
    1. y = (x+1)(x+2)(x-3)(x+4)
    The curve opens up , and has x-intercepts at
    x = -1,-2,3, and 4 , so it is easy to see that there must be 2 mins and 1 max

    2. y = (x-2)(x-3)(x^2 + 4)

    3. y = (x-10)(x^3-3)

    Play around with different quartics on this webpage, and you can see the different cases.

    y = x^4
    y = x^4 + x^3
    y = x^4 + x^3 + x^2
    now change some of the signs .
    Have some fun with math.

    1. 👍 0
    2. 👎 2

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus Please Help

    A continuous function f, defined for all x, has the following properties: 1. f is increasing 2. f is concave down 3. f(13)=3 4. f'(13)=1/4 Sketch a possible graph for f, and use it to answer the following questions about f. A. For

  2. Calculus

    Find the formula for a function of the form y=Asin(Bx)+C with a maximum at (1.5,1), a minimum at (4.5,−11), and no critical points between these two points.

  3. Calculus

    Suppose f '' is continuous on (−∞, ∞). (a) If f '(1) = 0 and f ''(1) = −1, what can you say about f ? 1)At x = 1, f has a local maximum. 2)At x = 1, f has a local minimum. 3)At x = 1, f has neither a maximum nor a minimum.

  4. Pre-Cal (polynomials)

    what is the general relationship between the degree of a polynomial function and the number of "bends" or relative maximum and minimum points in the graph?

  1. Calculus (pleas help!!!)

    Find the formula for a function of the form y=Asin(Bx)+C with a maximum at (0.5,0), a minimum at (1.5,−4), and no critical points between these two points.


    Determine whether the quadratic function has a minimum or maximum value.Then find the coordinates of the minimum or maximum point. f(x)=2x^2-4x

  3. Please check my Algebra

    Determine the maximum possible number of turning points for the graph of the function. f(x) = 8x^3 - 3x^2 + -8x - 22 -I got 2 f(x) = x^7 + 3x^8 -I got 7 g(x) = - x + 2 I got 0 How do I graph f(x) = 4x - x^3 - x^5?

  4. calculus

    Below is the graph of f '(x), the derivative of f(x), and has x-intercepts at x = -3, x = 1 and x = 2 and a relative maximum at x = -1.5 and a relative minimum at x = 1.5. Which of the following statement is true? (it's a positive

  1. Algebra

    Consider the quadratic function f(x) = – x^2 + 10x – 26. Determine whether there is a maximum or minimum value and find that value.

  2. PreCalc

    The temperature T(t) varies sinusoidally on a certain day in December. The minimum temperature is 35 degrees Fahrenheit at midnight. The maximum temperature is 50 degrees Fahrenheit at noon. Let t be the number of hours since

  3. Calculus

    Use analytical methods to find the exact global maximum and minimum values of the function f(x)=8x-ln(4x) for x >0. If a global maximum or minimum does not exist, enter the word NONE. For the global maximum at x=none, But for the

  4. Algebra2

    Complete parts a – c for each quadratic function. a. Find the y-intercept, the equation of the axis of symmetry and the x-coordinate of the vertex. b. Make a table of values that includes the vertex. c. Use this information to

You can view more similar questions or ask a new question.