y = 9ln(x)
<span>y' = 9x^-1 =9/x</span>
y'' = -9x^-2 =-9/x^2
curvature k = |y''| / (1 + (y')^2)^(3/2)
<span>= |-9/x^2| / (1 + (9/x)^2)^(3/2)
= (9/x^2) / (1 + 81/x^2)^(3/2)
= (9/x^2) / [(1/x^3) (x^2 + 81)^(3/2)]
= 9x(x^2 + 81)^(-3/2).
To maximize the curvature, </span>
we find where k' = 0. <span>
k' = 9 * (x^2 + 81)^(-3/2) + 9x * -3x(x^2 + 81)^(-5/2)
...= 9(x^2 + 81)^(-5/2) [(x^2 + 81) - 3x^2]
...= 9(81 - 2x^2)/(x^2 + 81)^(5/2)
Setting k' = 0 yields x = ±9/√2.
Since k' < 0 for x < -9/√2 and k' > 0 for x >
-9/√2 (and less than 9/√2),
we have a minimum at x = -9/√2.
Since k' > 0 for x < 9/√2 (and greater than 9/√2) and
k' < 0 for x > 9/√2,
we have a maximum at x = 9/√2. </span>
x=9/√2=6.36
<span>y=9 ln(x)=9ln(6.36)=16.66</span>
the
answer is
(x,y)=(6.36,16.66)
Answer:
Step-by-step explanation:
(((22•5ax2) + 25ax) + 15a) - 5 = 0
Step 2 :
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
20ax2 + 25ax + 15a - 5 =
5 • (4ax2 + 5ax + 3a - 1)
Equation at the end of step 3 :
5 • (4ax2 + 5ax + 3a - 1) = 0
Step 4 :
Equations which are never true :
4.1 Solve : 5 = 0
Answer:4x^2+22x-12
Step-by-step explanation:
height=(2x+12)
base=(4x-2)
Area of =(base x height)/2
Area of =((4x-2)(2x+12))/2
Area of =(8x^2+48x-4x-24)/2
Area of =(8x^2+44x-24)/2
Area of =4x^2+22x-12
m=-(5/4)
From left to right, (1,3) is first and then comes (5,-2). Always remember when finding slopes without equations, the rule is RISE over RUN, to the numerator and denominator, respectively.
The y value of the second coordinates becomes negative which is unlike the y value in the first coordinates, which means our slope is downward, meaning it has a negative sign in front.
In every slope, there’s a numerator, being the rise, and a denominator, being the run.
To find the rise, we must look at the y values. Starting at 3 going to -2 has a space of 5 units, making that our numerator.
To find the run, the first x value is 1 and the second is 5, making a space of 4, which is out denominator.
With these two numbers and the negative sign, we get -(5/4) as our slope.
