Chapter 7 Differential Calculus

Section 7.5 Applications

7.5.3 Exercises

With the following exercise the elements of the curve analysis method can be trained:
Exercise 7.5.1
Führen Sie für die Funktion f(x)=- x3 -6 x2 -7 eine vollständige Kurvendiskussion durch.

Exercise 7.5.51
Carry out a complete curve analysis for the function f with f(x)=(2x- x2 )ex and enter your results into the input fields.  
Maximum domain:
(as an interval (a;b)) .
Set of intersection points with the x-axis (zeros of f(x)):
(as a set {a;b;c }, only x-components) .
The y-intercept is at y = .
Symmetry: The function is
  axially symmetric with respect to the y-axis,
  centrally symmetric with respect to the origin.

Limiting behaviour: For x, the functions values f(x) tend to
, and for x-, they tend to .
Derivatives: We have f'(x) =
and f''(x) =
Monotony behaviour: The function is monotonically increasing on the interval
and monotonically decreasing otherwise.
Extremal values: The point x1 =
is a minimum point and the point x2 =
is a maximum point.
Inflexion points: The set of inflexion points consists of

(as a set, roots can be entered) .
Sketch the graph and compare your result to the sample solution.