The inflection points of the function x^4 + 13x³ - 21x² + x are given as follows:
x = -0.5 and x = 7.
<h3>What are the inflection points of a function?</h3>
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
#SPJ1