A stream gradient is the grade measure by the ratio of drop in elevation of a stream. It is expressed as feet per mile.
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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.
It's 2. your equation is y=mx+b, so the gradient, or slope, is the "m" in the equation.
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>
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.
It is sometimes called the gradient.