We have been given in a cohort of 35 graduating students, there are three different prizes to be awarded. We are asked that in how many different ways could the prizes be awarded, if no student can receive more than one prize.
To solve this problem we will use permutations.
We know that formula for permutations is given as
On substituting the given values in the formula we get,
Therefore, there are 39270 ways in which prizes can be awarded.
First of all, we compute the points of interest, i.e. the points where the curve cuts the x axis: since the expression is already factored, we have
Which means that the roots are
Next, we can expand the function definition:
In this form, it is much easier to compute the derivative:
If we evaluate the derivative in the points of interest, we have
This means that we are looking for the equations of three lines, of which we know a point and the slope. The equation
is what we need. The three lines are:
This is the tangent at x = -2
This is the tangent at x = 0
This is the tangent at x = 1