y = (3x + 1)⁵(3 - x)³
The stationary points are where dy/dx = 0
Note the use of:
If u and v are functions of x:
d/dx (uv) = v du/dx + u dv/dx
d/dx uⁿ = n uⁿ⁻¹ du/dx
dy/dx = (3 - x)³ d/dx (3x + 1)⁵ + (3x + 1)⁵ d/dx (3 - x)³
= (3 - x)³ 5 (3x + 1)⁴ d/dx (3x + 1) + (3x + 1)⁵ 3 (3 - x)² d/dx (3 - x)
= 5 (3 - x)³ (3x + 1)⁴ 3 + 3 (3x + 1)⁵ (3 - x)² (-1)
= 3 (3x + 1)⁴ (3 - x)² (5 (3 - x) - (3x + 1))
= 3 (3x + 1)⁴ (3 - x)² (15 - 5x - 3x - 1)
= 3 (3x + 1)⁴ (3 - x)² (14 - 8x)
= 6 (3x + 1)⁴ (3 - x)² (7 - 4x)
→ 3x + 1 = 0 → x = -1/3
or 3 - x = 0 → x = 3
or 7 - 4x = 0 → x = 7/4
y = (3x + 1)^5*(3 - x)^3dy/dx = 5* (3x + 1)^4*3*(3 - x)^3 - 3*(3x + 1)^5*(3 - x)^2
= 3*(3x + 1)^4*(3 - x)^2*[5*(3-x) - (3x + 1)]
= 6*(3x + 1)^4*(3 - x)^2*(7 - 4x)
Then the stationary points are reached when dy/dx = 0.
So, solving dy/dx = 0 gives
x = -1/3
x = 7/4
x = 3.
Y Equals X PointsAll points that has the same y coordinates as x coordinates are on the y=x line.
I believe it is 72 points. 95 percent sure.
3 equal points in a triangle??
It goes into decimal points, it equals 2.25
(4,2), (2,1),(-2,-1)
Stationary waves.
Five points equals .5 carats where one carat equals 1.00 points.
Abc is a triangle in which points p and r are such that ap equals pr equals rb also points q and s are on ac such that aq equals qs equals sc show that 3pq equals bc?
Motion movement and changes
A reference point is anything that is stationary. So, if you are on a train you know you have left the station because you moved away from the platform. Hence the platform was stationary.
No, but it can result in standing waves where some points are stationary.
It is the same as sin(x) but stretched by 5 in the y-directioni.e. the x-intercepts are at 0, pi and 2pi (or 0, 180, 360 in degrees)the y-intercept is at 5 and all of the stationary points are at either 5 or -5.
L points also known as Lagragian points, Libration points and Lagrance points. the L points are the five positions in an orbital configuration where a small object affected only by gravity can theoretically be stationary relative to two larger objects (such as a satellite with respect to the Earth and Moon).
That's all down to how hard you're riding. Most people will use more effort when riding IRL than riding stationary bikes.
Points on a Compass?
Since there are no "following" points, none of them.
1 ounce equals 3 points