Dr. J's Maths.com
Where the techniques of Maths
are explained in simple terms.

Exponential functions - Applications of differentiation - max/min questions.
Test Yourself 1.


 

Curves. 1. For the function y = x2 ex:

(i) find the coordinates of all stationary points and determine their nature.

(ii) Describe the shape of the curve as x approaches negative infinity.

(iii) Sketch the curve clearly labelling stationary points and intercepts.
  2. Find the set of values for x for which the function f(x) = xe-x is both decreasing and concave down.
  3.
2D shapes 6.

The diagram above shows the curve .


Both D and C both lie on the x-axis and OC = OD = L.

(i) Explain why the length of BC is .

(ii) Show that the area of the rectangle is .

(iii) Find the value for L for which ABCD has a maximum area.