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Max/Min. Functions
(i) Give the function a suitable symbol (usually y) if not already specified in the question.
(ii) Ensure the function is written in terms of a single variable (usually x). If not, use extra information supplied to achieve this.
(iii) Do
, SET = 0 and solve to get the stationary (turning) point(s). This is the hard part.(iv) Find the second derivative
and plonk the stationary points (SP) into it.If at an SP:
then the SP is a local min.If at an SP:
then the SP is a local max.(v) Plonk the SP(s) into the original function y to get the max. and/or min. value(s) of the function.
(b) Types of function to be treated.
The functions to be treated are:
(i) Algebraic (Al)
(ii) Exponential (Exp)
(iii) Logarithmic (Log)
(iv) Trigonometric (Trig)
Example 1 (Al)
Find the local max. and local min. of
if any.Solution
Example 2 (Expo)
Find the local maxima/local minima of
if any.e - ln trick: When e and ln come together they cancel each other out. This is very useful when solving expo and log equations. So
and 
Solution
Example 3 (Log)
Find the local max/ local min. of
if any.Solution
Example 4 (Trig)
Find the local maximum/local minimum of
if any.Solution
