SOLUTION: Please check my work for max/min problem. Find the max/min of: f(x) = 2x^3 - 3x^2 + 6 of f on [-1,1] f'(x) = 6x^2 - 6x f'(x) = 6x(x-1) therefore, x = 0 & x = 1 and includi

Question 999602: Please check my work for max/min problem.
Find the max/min of:
f(x) = 2x^3 - 3x^2 + 6 of f on [-1,1]
f'(x) = 6x^2 - 6x
f'(x) = 6x(x-1)
therefore, x = 0 & x = 1 and including the boundary x = -1
testing...
f"(x) = 12x - 6
f"(0) = 12(0) - 6 = -6 < 0, MAX value occurs at x = 0
f'(1) = 12(1) - 6 = +6 > 0, MIN value occurs at x = 1
f"(-1) = 12(-1) - 6 = -18 < 0, MAX value occuras at x = -1
This confuses me because now I have one MIN value that occurs at x = 1, but this isn't actually the value of the MIN just where it occurs right?
And then I have two MAX's which one is the real max? because I think I am only dealing with rel max/min so I don't think two would make sense.
Plese explain
Thank you

Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Yes, and are two extrema values.
is the relative maximum.
is the relative minimum.
However since you're in an interval, you need to check the endpoints and there is a definite min and max.

So in the interval, the minimum occurs at and the maximum occurs at .
.
.
.

.
RELATED QUESTIONS
Please check my answers: Q: Let f(x) = 2x^3 - 3x^2 + 6. Find the max and min values of (answered by jim_thompson5910)

What is the process for finding max/min for functions? I have this function: f(x) = 2x^3 (answered by ikleyn)

1) Find the vertex, the line of symmetry, and the max or min value of f(x). Graph the... (answered by solver91311)

Find the absolute max and min values of f(x) = 1 + 96x - 2x^3 on the interval [0,5]. I (answered by ikleyn)

f(x)=x^2-6x-3 vertex? equation of line of symmetry? max/min of f(x)? is the value of, (answered by John10)

find the vertex, the line of symetry, and the maximum or minimum value of f(x). graph... (answered by Edwin McCravy)

Find the vertex, line of symmetry, min or max and graph.... (answered by lwsshak3)

find the vertex, line of symmetry, min or max and graph.... (answered by ewatrrr)

f(x)=1/2(x+6)^2+6 Find vertex, line of symmetry max/min and... (answered by lwsshak3)