Answer: an approximate upper bound for the function is 0.9282
Explanation:
To find the upper bound of the function f(x) = 3x^4 - 7x^3 + 5x - 3, we need to determine its maximum value, which occurs at the peak of the graph.
To do this, you can find the critical points by taking the derivative of the function and setting it equal to zero:
f(x) = 12x^3 - 21x^2 + 5
Next, solve for x.
12x^3 - 21x^2 + 5 = 0
This equation can be challenging to solve directly, but you can use numerical methods or a graphing calculator to approximate the solutions. These critical points will be where the function has local extrema.
Once you find the critical points, evaluate the function f(x) at these points and compare the values to find the upper bound. The highest value among these critical points will be the upper bound of the function.
Please note that solving for the critical points and finding the exact upper bound may require numerical methods because it's a polynomial of a relatively high degree.