Critical points occur where the gradient is zero. This is guaranteed whenever
and either
or
.
The Hessian matrix for this function looks like
and has determinant
Maxima occur whenever the determinant is positive and
. Minima occur whenever both the determinant and
are positive. Saddle points occur whenever the determinant is negative.
At
, you have a saddle point since the determinant reduces to -324, so
is the saddle point.
At
, the determinant is
and
, so
is a local maximum.
No other critical points remain, so you're done.
Answer:
Step-by-step explanation:
Given
See attachment for wedge
Required
The sample space of the wedge is:
The outcomes greater than 5 are:
So, the probability is:
This gives:
Answer:
Step-by-step explanation:
<u>Equation of a Polynomial</u>
Given the roots x1, x2, and x3 of a cubic polynomial, the equation can be written as:
Where a is the leading coefficient.
We know the three roots of the polynomial -6, -3, and 1, thus:
Since the y-intercept of the polynomial is y=90 when x=0:
90=a(0+6)(0+3)(0-1)
90=a(6)(3)(-1)=-18a
Thus
a = 90/(-18) = -5
The polynomial is:
We must write it in standard form, so we have to multiply all of the factors as follows:
I hope this helps you
-3n÷-3 < -18÷-3
n>6
Answer:
Noncollinear points
Step-by-step explanation:
Collinear points lie on the same line. Noncollinear points are the opposite.
