Question

Find all the roots of the given function. Use preliminary analysis and graphing to find good initial approximations.

f(x) = cos(4x) - 6x² + 9x

The function has a root when x ≈ ... (the value of x is not provided, but it's where the root occurs).

Answer 1

To find the roots of the given function f(x) = cos(4x) - 6x² + 9x, we can use preliminary analysis and graphing to find good initial approximations.

Step-by-step explanation:

To find the roots of the given function f(x) = cos(4x) - 6x² + 9x, we can use preliminary analysis and graphing to find good initial approximations. First, let's graph the function and observe where it intersects the x-axis. This will give us initial approximations for the roots.

Upon graphing the function, we find that it intersects the x-axis approximately at x ≈ -0.8, x ≈ 0.5, and x ≈ 1.2. These are the initial approximations for the roots. Now, we can use numerical methods or calculators to find accurate values for the roots.

Note: The approximate values of the roots may vary depending on the precision of the graphing software used.