Question

Required information Consider the function f(x)=−1.5x 6 −2x 4+12x Differentiate the given function and then use the bisection method to solve for the maximum f(x) and the corresponding value of x. Iterate until ε a=1%. (Round the final answer to four decimal places.) The maximum of the given function is at x=

Answer 1

To solve for the maximum of the given function f(x) = -1.5x^6 - 2x^4 + 12x, we can differentiate the function and use the bisection method. The bisection method involves splitting the interval and checking for sign changes to find the root or maximum. Iteration is done until a desired level of accuracy (εa = 1%) is reached.

Step-by-step explanation:

To find the maximum of a function, we need to differentiate it and find the critical points where the derivative is equal to zero. So, let's start by differentiating f(x) = -1.5x^6 - 2x^4 + 12x.

Taking the derivative, we get f'(x) = -9x^5 - 8x^3 + 12.

Now, we can use the bisection method to find the maximum of the function. The bisection method involves splitting the interval and checking for sign changes to find the root or maximum. We will start by choosing an interval where the function changes sign, such as (-10, 10).

We will then iterate until we reach a desired level of accuracy (εa = 1%). The final answer rounded to four decimal places will give us the maximum of the function and the corresponding value of x.