Hello there!
To find the increasing intervals for this graph just based on the equation, we should find the turning points first.
Take the derivative of f(x)...
f(x)=-x²+3x+8
f'(x)=-2x+3
Set f'(x) equal to 0...
0=-2x+3
-3=-2x
3/2=x
This means that the x-value of our turning point is 3/2. Now we need to analyze the equation to figure out the end behavior of this graph as x approaches infinity and negative infinity.
Since the leading coefficient is -1, as x approaches ∞, f(x) approaches -∞ Because the exponent of the leading term is even, the end behavior of f(x) as x approaches -∞ is also -∞.
This means that the interval by which this parabola is increasing is...
(-∞,3/2)
PLEASE DON'T include 3/2 on the increasing interval because it's a turning point. The slope of the tangent line to the turning point is 0 so the graph isn't increasing OR decreasing at this point.
I really hope this helps!
Best wishes :)
4 quarters 1 dime
11 dimes
110 pennies
2 half dollars 1dime
22 nickels
1 half dollar 2 quarters 10 pennies
1quater 25 pennies 1 half dollar 2 nickels
Answer:
Corresponding: The top left, The bottom left
Alternate interior: Bottom right
Alternate exterior: Top middle
None of these: Top right
Step-by-step explanation:
4x=3y+3 and 6y= 8x+ 36 and y=3x-1 and y= 6- x/3
4x=3y+3 and 6y= 8x are parallel and y=3x-1 and y= 6- x/3 are perpendicular.
See the attached plot for answer.
-4>4(2-w)>-12
-1>2-w>-3
-3>-w>-5
3<w<5
~~~~~~~~~~~~~~~~~~~~~~~~~
If you're wondering why the sign changes when we divided (or multiplied) by a negative value, let's give a simpler example:
-5<-2 -> -5 is less than -2. That expression makes sense. Now multiply that by -1. You get 5<x<2. Does that make sense? No. When you switch the signs of everything, the sign will always get switched.
