Find the value of x at which the function has a possible relative maximum or minimum point. (Recall that e Superscript x is pos
1 answer:
Answer:
x= -11/4 is a maximum.
Step-by-step explanation:
Remember that a function has its critical points where the derivative equal zero. Therefore we need to compute the derivative of this function and find the points where the derivative is zero. Using the chain rule and the product rule we get that
And then we get that if then
. So it has a critical point at
.
Now, if the second derivative evaluated at that point is less than 0 then the point is a maximum and if is greater than zero the point is a minimum.
Since
x= -11/4 is a maximum.
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Answer:
(x - 2)² + (y + 3)² = 32
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
The centre of the circle is at the midpoint of the diameter
Calculate the centre (x, y ) using the midpoint formula
(x, y ) = ( ,
)
with (x₁, y₁ ) = (- 2, 1) and (x₂, y₂ ) = (6, - 7)
(x , y ) = ( ,
) = (
,
) = (2, - 3)
The radius is the distance from the centre to either of the endpoints
Calculate the radius using the distance formula
r =
with (x₁, y₁ ) = (2, - 3) and (x₂, y₂ ) = (- 2, 1)
r =
=
=
=
=
Then equation of circle is
(x - 2)² + (y - (- 3) )² = ( )² , that is
(x - 2)² + (y + 3)² = 32