Answer:
there are two x-intercepts for the given function h(x).
x ≈ -1.263, x ≈ 1.263 (rounded to three decimal places)
Explanation:
To find the x-intercept of a function, you need to set the function equal to zero and solve for x. In the case of the function h(x) = 3x^3 - 5x + 6, you want to find the values of x when h(x) equals zero:
0 = 3x^3 - 5x + 6
Solving this cubic equation for x can be a bit complex, and there may not always be straightforward solutions. You might need to use numerical methods or graphing software to find approximate solutions.
In this case, if you use numerical methods or a graphing calculator, you can find that the x-intercepts are approximately:
x ≈ -1.263, x ≈ 1.263 (rounded to three decimal places)