Question

Let f:[-3,2] --> r be a differentiable function such that 0

Answer 1

The given differentiable function has a positive but bounded rate of change in its domain.

Step-by-step explanation:

Based on the given information, we have a differentiable function f(x) defined on the interval [-3,2] such that 0 < f'(x) < 20 for all x in (-3,2).

Since f(x) is differentiable, it means that the function is continuous and has a well-defined derivative at every point in its domain. The condition 0 < f'(x) < 20 indicates that the rate of change of the function is positive but less than 20 for all x in the interval (-3,2). In other words, the function is increasing but not too rapidly.

For example, if we consider a specific point x = 0 in the interval [-3,2], the derivative f'(0) represents the instantaneous rate of change of the function at that point. Since 0 < f'(x) < 20, it means that the function is getting steeper, but it does not have a very steep slope. This condition is satisfied for all points in the interval (-3,2).