A fixed point of f is a value of x that satisfies the equation f(x) = x; it corresponds to a point at which the graph of f intersects the line y = x. Find all the fixed points of the function. Use preliminary analysis and graphing to determine good initial approximations. Round approximations to six decimal places.
-f(x) = 3 sin x on [0, 2π]
A) x = 0 and x $\approx$ 2.278863
B) x = 0 and x $\approx$ 2.389974
C) x = 0 and x $\approx$ 2.167752
D) x = 0 and x $\approx$ 1.756641

Question

Quizplus · Accepted Answer

The fixed points occur where $f(x) = x$, so we solve $3\sin(x) = x$. At $x = 0$, the equation holds. For the other solution, graphing or numerical methods are needed due to the transcendental nature of the equation. The approximation $x \approx 2.278863$ is found using such methods, making choice A correct.

A Fixed Point of F Is a Value of X ≈\approx≈

A Fixed Point of F Is a Value of X $\approx$