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

Functions - Logarithmic - Differentiation.
Applications - Test Yourself 1.


 

The questions on this page focus on:

  1. determining gradients;
  2. equations of tangents and normals;
  3. maximum and minimum questions;

 
Gradients 1.
  2.
  3.
Tangents and normals 4. .
  5.
  6.
  7.

(i)

(ii)

(iii) On the sketch, draw in the tangent and the normal -
especially to mark in the point Q.
  8. .
  9.
  10.
Maximum and minimum questions 11.
 

12. (i) Draw the graphs of y = ln(x - 1) and y = x on the same set of axes.

(ii) D = x - ln (x - 1).

(iii)

(iii) Minimum distance = 2 - ln(2 - 1) = 2.
 

13.

  14.
 

15.