To find on what interval the temperature is positive, we need to find the values of x for which f(x) is greater than zero.
The function f(x) is defined as:
f(x) = -3|x - 4.7| + 2
Since the absolute value of any real number is always non-negative, we can see that f(x) will be positive only if the expression inside the absolute value bars is less than 2/3. So, we can set:
-3|x - 4.7| + 2 > 0
Solving for |x - 4.7|, we get:
|x - 4.7| < 2/3
This means that x must be within 2/3 units of 4.7. So, the interval on which the temperature is positive is:
4.7 - 2/3 < x < 4.7 + 2/3
Simplifying, we get:
4.0333 < x < 5.3667
Therefore, the temperature is positive on the interval (4.0333, 5.3667).