Saxon Math Calculus

• Saxon math calculus deals with solving basic calculus problems for test preparation. Most of the Saxon’s math book deals with solving test problems for exam preparation. Saxon’s Calculus mainly deals with the differentiation of functions with one or more variables. Calculus can be divided into two parts namely differential calculus and integral calculus. Mostly Saxon’s calculus test involves in solving differential problems. The following are the test problems in math calculus solved by Saxon.

  
  

  Example problems on saxon math calculus:

  The following are the Saxon’s test problems in calculus with detailed solution.
  

  Ex:1 Solve the given function by differentiation f(u) = u ³ – 48u + 10

  Sol: The given function f(u) is the set of all real numbers. The first derivative f' (u)is given as
  f '(u) = 3 u ² - 48
  f '(u) is defined for all real numbers. Let us now solve f '(u) = 0
  3 u ² - 48 = 0
  Add 48 on both sides,
   3 u ² – 48 + 48 = 48
  3 u ² = 48
  u ² = 16
  u = 4 or u = -4
  Since u = 4 and u = -4 are in the domain of f so these both are  critical numbers.
  
  Ex:2 Solve the given function by differentiation. f(u) = | u - 8 |
  Sol:
  The domain of f(u) is the set of all real numbers. Let us use the fact sqrt (s ²) = | s | to modify function f as follows
  f(u) = sqrt (s ²) , with s = u - 8
  Using the chain rule, f '(u) is given by
  f '(u) = (1/2) 2 s s'(u) / | s |
  Since s '(u) = 1, f '(u) simplifies to
  f '(u) = (u - 8) / | u - 8 |
  f ' is undefined at u = 8 and 8 is in the domain of f. u = 8 is a critical number of function f given above.
  
  Q:3 Determine the critical number(s) of the absolute value function f given by f(x) = | x - 8 |
  Sol: The domain of f is the set of all real numbers. Let us use the fact sqrt (u ²) = | u | to modify function f as follows
  f(x) = sqrt (u ²) , with u = x - 8
  Using the chain rule, f '(x) is given by
  f '(x) = (1/2) 2 u u'(x) / | u |
  Since u '(x) = 1, f '(x) simplifies to
  f '(x) = (x - 8) / | x - 8 |
  f ' is undefined at x = 8 and 8 is in the domain of f. x = 8 is a critical number of function f given above.
  
  Practice problems on saxon math calculus:
  
  The Saxon math test problems in calculus are given below for practice.
  Q:1 Solve the given function by differentiation. f(x) = u ⁴ - 108u + 100
  Ansr:  u = 3 or u = -3
  
  Q:2 Solve the given function by differentiation  f(u) = | u - 7 |
  Ans:  f ' is undefined at u = 7 and 7 is in the domain of f. u = 7 is a critical number of function f given above.