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Why the second derivative negative for Maxima?
When you solve for the 2nd derivative, you are determining whether the function is concave up/down. If you calculated that the 2nd derivative is negative, the function is concave down, which means you have a relative/absolute maximum, given that the 1st derivative equals 0. To understand why this is, think about the definition of the 2nd derivative. It is a measure of the rate of change of the gradient. At a maximum, the gradient starts positive, becomes 0 at the maximum itself and then becomes negative, so it is decreasing. If the gradient is going down, then its rate of change, the 2nd derivative, must be negative.
How do you find the gradient of y equals 2x plus 3?
It's 2. your equation is y=mx+b, so the gradient, or slope, is the "m" in the equation.
What is gradient formula?
Assume you want to know what is the formula of the gradient of the function in multivariable calculus. Let F be a scalar field function in n-dimension. Then, the gradient of a function is: ∇F = <fx1 , fx2, ... , fxn> In the 3-dimensional Cartesian space: ∇F = <fx, fy, fz>
What is meant by negative gradient of a quantity?
The gradient of a quantity is the greatest rate at which it changes as you move in different directions from where you are now. If the quantity has a negative gradient, that means that the quantity decreases in that direction. A great example of a negative gradient is the elevation of the land at a point on a road that has a hill on one side and a cliff on the other side. The greatest rate at which the elevation changes is in the direction off the edge of the cliff, and it's negative in that direction.
What is the steepness of a line graph called?
It is sometimes called the gradient.
In a typical stream where the gradient in steep the discharge is?
In a typical stream where the gradient is steep the discharge is small.
In a typical stream where the gradient is steep the discharge .?
In a typical stream where the gradient is steep the discharge is small.
Stream gradient role on stream velocity?
Stream gradient, or the slope of the stream channel, affects stream velocity by influencing the speed at which water flows downstream. A steeper stream gradient typically results in a faster water flow velocity, as the force of gravity pulls water downhill more strongly. Conversely, a gentler stream gradient leads to slower water flow velocity.
What is a channel of a stream?
Gradient
In a typical stream where the gradient is steep the discharge is?
In a typical stream where the gradient is steep the discharge is small.
The vertical drop of a stream channel over a certain distance is called the?
The vertical drop of a stream channel over distance is known as the Gradient.
What is the definition of stream velocity?
Stream velocity is the speed at which water flows in a stream or river. It is typically measured in units of distance per time (e.g. meters per second) and can vary based on factors such as gradient, channel shape, and discharge.
What is the steepness of a stream channel?
The steepness of a stream channel is typically measured by its gradient, which is the rate at which the elevation of the channel changes over a certain horizontal distance. The steeper the gradient, the faster the water will flow and the more erosive power the stream will have.
What is the definition of stream gradient?
A) the distance traveled by water in a channel times a drop in elevation b) the drop in elevation of a stream divided by the distance the water travels c) the water pressure at the bottom of the stream divided by the stream's width d) the increase in discharge of a stream per unit drop in elevation
What is a stream slope called?
It is called the gradient.
What happens to the gradient of a stream as one gets closer and closer to the head of the stream?
increases
What happens to stream gradient as it moves downstream?
it decreses
