extrema

posted by .

The function is given as
y = 7x^3 - 8x^2 -16x +15

The max is at x = -4/7 & min is at x = 4/3

How do I know that it is local max&min or absolute max &min? (graphing calculator is not allowed)

You know that it's a local minimum and maximum because the x^3 term approaches positive infinity as x goes to infinity and negative infinity as x goes to minus infinity.

explanation please?

Generally if the domain or interval is not given, how do we assume the extrema is local or absolute?

If the domain is not given then you can assume it is the maximal possible domain. In this case it is the entire real axis, but in some cases you have to exclude regions where the function is not defined.

You then determine the range of the function. To this this you need to know the properties of the function. In this case it is simple; you are dealing with a polynomial function. The x^3 term dominates for large positive and negative x.

So, you already know by just looking at the function that the range of the function is from minus infinity to plus infinity (note that (-x)^3 = - x^3 ).

This means that the points where the derivatives are zero can't be absolute maxima or minima.

If you have a polynomial of even degree, e.g. with a x^4 term then, depending on the sign of the x^4 term, the range extends either from some minumum value to plus infinity or to negative infinity, but not from minus to plus infinity.

If the range extends to plus infinity, then you can only have local maxima, but a minimum can be global. You should then list al the minima and examine at which of these the value of the function is the least.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. MAth

    If 1 gallon (gal) of water weighs 8.34 pounds (lb), how much does 3.75 gal weigh?
  2. Calculus

    Find the values for which f(x) = x^10-10x and if 0 (less than or equal) to x (which is less than or equal to) 2. a) f(x)has a local max or local min. Indicate which ones are max and which are mins. b) f(x) has a global max or global …
  3. Calculus

    What is the absolute max and absolute min of 3+13 |t-8| for -1 <= t <= 11?
  4. PreCalc

    y =( (C-A)/2 ) sin( (X - (A - ( (C - A)/2 ) ) )( pi/(C-A) ) ) + (B - ( (B-D)/2 ) How do I rearange this for this equation for the all of the variables including A, B, C, D, X were pi is the greek leter pi if you didn't notice this …
  5. calculus

    I don't understand how to do this? I don't know the steps on how to do it! Can you please just tell me the steps?
  6. Calculus

    Find any absolute max/min and local max/min for the function f(x)=x^3-4x+5 on the interval [0,5). Made sure to prove that these points are max/min values. This is what I did so far. f'(x)=3x^2-4=0 3x^2=4 x= 2/sqrt3 The -2/sqrt3 is …
  7. math

    how to solve this problem: max min(x-y)..... here where the max have written, under it x>=0 is also given. also under min y>=0 is given. Also tell that is this is equals to min max(x-y) ?
  8. calculus

    Sketch the curve y = x^3 - 12x^2 + 36x I already did the question properly it is concave down at (0,4) and concave up at (4,infinity) I found the abs max to be (2,32) and abs min to be (6,0) What I wanted to know is when labeling the …
  9. Math

    Find the critical points and the interval on which the given function is increasing or decreasing, and apply the First Derivative Test to each critical point f(x)= (7/4)x^4+(28/3)x^3+(-63/2)x^2-252x critical points in increasing order: …
  10. Algebra 2

    Please help super confused!!! Which points are the best approximation of the relative maximum and minimum of the function?

More Similar Questions