Question

Consider the function y = 3x5 – 25x3 + 60x + 1. Find the critical points of this function.

So I got 1 and 2 as the critical points..but I feel like I did something wrong, is this right?

Answer 1

I am sure you meant:
y = 3x^5 - 25x^3 + 60x + 1
dy/dx = 15x^4 - 75x^2 + 60
= 0 for your critical values
3x^4 - 15x^2 + 12 = 0
x^4 - 5x^2 + 4 = 0
(x^2 - 1)(x^2 - 4) = 0
x^2 = 1 or x^2 = 4
x = ± 1 OR x = ± 2

sub in those values of x in the original to get the mataching y values of the critical points.

Some would consider the inflection points in the list of critical points

y'' = 60x^3 - 150x
= 0 for points of inflection
6x^3 - 15x = 0
2x^3 - 5x = 0
x(2x^2 - 5) = 0
x = 0 or x = ± 5/2
continue to find the points of inflection

Answer 2

So the points would be -1,-2,1,2?

Answer 3

no, points consist of ordered pairs of two numbers.
±1 and ±2 are the x's of the points.

I told you what to do with those x's above, please read it.

Answer 4

it is -2, -1, 1, 2