Finding Critical Numbers; Finding the Extrema in the Interval; etc.

Related BrainMass Solutions

• Functions, derivatives, and critical numbers

  This shows how to find a function from the derivative and the graph of the derivative, as well as finding critical numbers and extrema.

• Differentiation : Find Local Extrema of a Function on an Interval

  First we need to find the critical numbers, i.e., roots of f'(x)=0.

• Differentiation : Locate the absolute extrema of the function : f(x) = √(4 - x^2)

  Use f to evaluate critical numbers and end points to find absolute extrema. Please see the attached file for the complete solution. Thanks for using BrainMass.

• Extrema and saddle points

  We calculate f_x = 2x - 3y f_y = -3x + 2y so the critical points (a, b) are solutions to 2a - 3b = 0 -3a + 2b = 0 in which case (a, b) = (0, 0) is the only solution.

• Series of Calculus Questions

  Find all the extrema in the interval [0, ] if y = x + sin x. 3. Find the absolute maximum and absolute minimum of f on the interval (-1,2]. 4. Consider .

• Finding relative extrema and inflection points

  100033 Finding relative extrema and inflection points. Find any relative extrema and inflection points of the functions y= x^2 lnx and y =x. See attached file for full problem description.

• Relative extrema

  219124 Finding Relative Extrema Find all relative extrema of the following function: f(x) = x^3 - 6x^2 +15. See the attached file. Please find the solution in the attachment.

• demand function

  Let us take some test values say x = 9, 11 Thus, profit function is increasing in the interval [0, 10.3764] and decreasing in the interval [10.3764, 20]. Production level will be maximum at x = 10.3764.

• Differentiation, Extrema of a Function

  The point to pay attention to is to have a critical point at x=0. It means f'(0)=f''(0)=0 at this point, but, in the simplest case f'''(0) is not 0.