The local minimum of function is an argument x for which the first derivative of function g(x) is equal to zero, so:
g'(x)=0
g'(x)=(x^4-5x^2+4)'=4x^3-10x=0
x(4x^2-10)=0
x=0 or 4x^2-10=0
4x^2-10=0 /4
x^2-10/4=0
x^2-5/2=0
[x-sqrt(5/2)][x+sqrt(5/2)]=0
Now we have to check wchich argument gives the minimum value from x=0, x=sqrt(5/2) and x=-sqrt(5/2).
g(0)=4
g(sqrt(5/2))=25/4-5*5/2+4=4-25/4=-9/4
g(-sqrt(5/2))=-9/4
The answer is sqrt(5/2) and -sqrt(5/2).
Answer:
As eq of line passing through 2 points is
y-y1 = (y2-y1)/(x2-x1) ][ x -x1)
where (X1,y1)( x2, y2) denotes points lying on line
substitute (X1 ,y1) by( -1,-2) and (X2,y2) by( 2,4)
y+2 = 6/3 )( x+1)
y+2= 2x +2
y = 2x is required equation
Answer:
81
Step-by-step explanation:
hope it helps
Answer:
x²/25 + y²/9 = 1 or 9x² + 25y² = 225
Step-by-step explanation:
We have two points which is y intercepts (0,-3) and (0,3).
We know that the major axis is 2a and secondary axis is 2b
These two points are vertical top of the ellipse which they give us value of half secondary axis b = 3
The length of major axis is 2a = 10 => a = 10/2 = 5 => a = 5
The equation of the ellipse is:
x²/a² + y²/b² = 1 or b²x² + a²y² = a²b²
When we replace value of a and b we get:
x²/5² + y²/3² = 1 or 3²x² + 5²y² = 5² · 3² and finally
x²/25 + y²/9 = 1 or 9x² + 25y² = 225
God with you!!!
Answer:
<em><u>z = -3</u></em>
Step-by-step explanation:
<u>Step 1: Simplify both sides of the equation.
</u>
z+7=−z+1
<u>Step 2: Add z to both sides.
</u>
z+7+z=−z+1+z
2z+7=1
<u>Step 3: Subtract 7 from both sides.
</u>
2z+7−7=1−7
2z=−6
<u>Step 4: Divide both sides by 2.
</u>
<u>2z</u> = <u>−6
</u>
2 2
z=−3
