**Differentiation Application Example
**

Lets assume that the student asked what the solution to the below question.
This equation has four unknowns, namely a, b, c and d and therefore four equations are needed to solve. The concepts you need to answer this question includes zeroes of a polynomial (Algebra Download), derivatives and stationary points (Differentiation Download).
You can solve this question by seeing the solutions to the given questions which use the same concepts.
(equation 1)
Hence .
Substituting in y gives:
What is the value of d in your question?
That is: .............................................. (equation 2) .............................................. (equation 3) Multiplying equation 2 gives: .............................................. (equation) Adding equations and 3 gives:
That is: .............................................. (A)
At what points the curve in your question cuts the x-axis?
when
.............................................. (equation 4) .............................................. (equation 2)
Adding equations 2 and 4 gives:
That is: .............................................. (B) We already obtained the equation A in question 2. .............................................. (A) Multiplying equation A by 0.8630 gives: .............................................. () Adding equations and B gives:
Substituting b, in equation A gives:
Substituting the values of a and b in equation 2 gives: .............................................. (equation 2)
Finally, substituting a, b, c in gives:
At what value of x, the curve in your question has a stationary (maximum, minimum or point of inflection)? |