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Teh
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View attachment 6135
View attachment 6136They want the curve in inequality form which i am not sure if i got it right
View attachment 6136They want the curve in inequality form which i am not sure if i got it right
MarkFL said:We are given:
\(\displaystyle y=2x^3-15x^2+24x\)
Now, to determine where the slope is decreasing, we need to find where the second derivative of $y$ is negative...what do you get for $y''$?
Teh said:y'' = 8x-15?
MarkFL said:We have:
\(\displaystyle y=2x^3-15x^2+24x\)
Now, using the power rule on each term, we get:
\(\displaystyle y'=6x^2-30x+24\)
And differentiating again:
\(\displaystyle y''=12x-30=6(2x-5)\)
So, we need to solve:
\(\displaystyle 2x-5<0\)
What do you get?
Teh said:\(\displaystyle x < \frac{5}{2}\)
No not really may you explain pleaseMarkFL said:Yes. (Yes)
Do you see the difference between a decreasing slope and a decreasing function? :D
The slope of a decreasing curve is a measure of how steep the curve is at any given point. It represents the rate of change of the curve as it moves downwards.
The slope of a decreasing curve is calculated by finding the change in the y-coordinates divided by the change in the x-coordinates between two points on the curve. This is represented mathematically as (y2 - y1) / (x2 - x1).
A negative slope on a decreasing curve represents a decrease in the value of the y-variable as the x-variable increases. This means that the curve is moving downwards from left to right.
The slope of a decreasing curve is directly related to the steepness of the curve. A larger slope value indicates a steeper curve, while a smaller slope value indicates a gentler curve.
No, the slope of a decreasing curve can never be positive. This is because a decreasing curve always has a negative slope, indicating a downward trend in the data. A positive slope would indicate an upward trend, which is not possible on a decreasing curve.