QuestionFind any relative extrema of the function. (Round your ar $$f(x)=\arctan (x)-\arctan (x-9)$$ relative maximum $(x, y)=(4.5,2.702 x)$

Studdy Solution
Calculate the function value at the critical point to find the relative maximum.
$$f(4.5) = \arctan(4.5) - \arctan(4.5-9)$$
$$f(4.5) = \arctan(4.5) - \arctan(-4.5)$$
Using the property $\arctan(-x) = -\arctan(x)$:
$$f(4.5) = \arctan(4.5) + \arctan(4.5)$$
$$f(4.5) = 2\arctan(4.5)$$
Using a calculator, approximate $\arctan(4.5) \approx 1.351$:
$$f(4.5) \approx 2 \times 1.351 = 2.702$$
The relative maximum is at $(x, y) = (4.5, 2.702)$.
The relative maximum of the function is at $(x, y) = (4.5, 2.702)$.