Question

Find the inflection points of ()=4+133−212+11.

Answer 1

The inflection points of the function x^4 + 13x³ - 21x² + x are given as follows:

x = -0.5 and x = 7.

What are the inflection points of a function?

The inflection points of a function y = f(x) are the values of the input x for which the second derivative of the function has a numeric value of zero.

The function in this problem is defined as follows:

x^4 + 13x³ - 21x² + x.

Applying the power of x rule, the derivatives of the function are given as follows:

• First derivative: y' = 4x³ - 39x² - 42x + 1.

• Second derivative: y'' = 12x² - 78x - 42.

The second derivative is a quadratic function with the coefficients given as follows:

a = 12, b = -78, c = -42.

Using a quadratic function calculator, the zeros of the second derivative, which are the inflection points of the function, are given as follows:

x = -0.5 and x = 7.

More can be learned about inflection points at brainly.com/question/14338487

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