Question

Find the maximum rate of change of f(s,t)=st at the point (0,3).

a) 3
b) 0
c) Undefined
d) Infinite

Answer 1

The maximum rate of change of the function f(s,t) at the point (0,3) is 3, which is the magnitude of the gradient at that point.

Step-by-step explanation:

The question asks for the maximum rate of change of the function f(s,t) = st at the point (0,3). This is found by calculating the gradient of the function and evaluating it at the given point. The gradient of f is the vector of partial derivatives, which is (∂f/∂s, ∂f/∂t).

Computing these partial derivatives gives (t, s). At the point (0,3), the gradient is (3, 0). The maximum rate of change of a function at a given point is the magnitude of the gradient at that point, which in this case is 3. Therefore, the maximum rate of change of the function f(s,t) at the point (0,3) is 3.