Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
Interpreting directional derivatives A function ƒ and a point P are given. Let θ correspond to the direction of the directional derivative.
a. Find the gradient and evaluate it at P.
b. Find the angles θ (with respect to the positive x-axis) associated with the directions of maximum increase, maximum decrease, and zero change.
c. Write the directional derivative at P as a function of θ; call this function g.
d. Find the value of θ that maximizes g(θ) and find the maximum value.
e. Verify that the value of θ that maximizes g corresponds to the direction of the gradient. Verify that the maximum value of g equals the magnitude of the gradient.
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