If f(x) = x^4 - 4x^3 + 10 find the relative extrema of the function and the
points of inflection of its graph. Also, sketch the graph of the function.
a. The x-value(s) of the relative minima of function f: ________________
b. The x-value(s) of the relative maxima of function f: _______________
c. The x-value(s) of point(s) of inflection of function f: _______________
Solution Preview
See attachment. I did this in mathematica and pasted it to word. If you want to try it in mathematica just cut and paste the code. Also, this web site might be helpful.
If f(x) = x^4 - 4x^3 + 10 find the relative extrema of the function and the
points of inflection of its graph. Also, sketch the graph of the function.
a. The x-value(s) of the relative minima of function f: ______3__________
b. The x-value(s) of the ...
Solution Summary
This solution is comprised of a detailed explanation to find the relative extrema of the function and the
points of inflection of its graph and sketch the graph of the function.
... The following points should be clearly labeled with their coordinates: i. x- and y-intercepts ii. local max/min iii. inflection point(s). 2. f(x) = 2x^2 / x^2-1 ...
... So stationary points are (-1/3, {23/27}) (max) and (-1,1) (min). The point of inflexion occurs exactly halfway between the two stationary points so x=(-1-3)/2 ...
... 6. For , use calculus to determine the location of: a. Any maximum or minimum points (tell which are max and which are min). b. Any inflection points. ...
... sketch the graph of y=f(x), and identify and local max or min and golobal ... x^2/(x-1) sketch the graph, identify all extrema, inflection pts, intercepts, and ...
... (ii) the maxima, minima and any points of inflection (iii) the values of x where the function is ... positive whenever x = 0, so there are no local max/min. ...
... derivative: At x = x2 , x4 , f ''( x) = 0 , so x2 and x4 are points of inflection. ... of f '( x) . Then when f ''( x) = 0 , f '( x) has local max or min. ...
... The critical points are when f'(x) = 0. ... Point of inflection occurs when f"(x) = 0. ... This shows how to determine max, min, intercepts, concavity, and increasing ...
