Question

Find the maximum value of the function y=x^4 - x^2 +13 on the interval [-1;2]

Answer 1

Answer: the maximum is 25.

Step-by-step explanation: a max/min can occur on the endpoints of a function and critical points of the function's derivative.

f(x)=x^4-x^2+13

f'(x)=4x^3-2x

The critical points of f'(x) occur when f'(x) is zero or undefined. f'(x) is not ever undefined in this case, so we just need to find the x values for when it's zero.

0=4x^3-2x

x=.707, -.707

Now that we have the critical points of f'(x) (.707 and -.707) and endpoints (-1 and 2), we can plug in these x values into the original function to determine its maximum. When you do this you'll find that the greatest y value produced occurs when x=2 and results in a max of 25.