Local max and min help needed!?!?

Question

Find local maximums and minimums for f(x) = x^2(2) - 4x + 4 on the interval 2 ≤ x ≤ 6

Answer 1

For local extrema, the derivative is zero
dy/dx = 4x -4 =0
or x =1. but it doesn't lie in the given domain range
Also, if you notice, the value of dy/dx is positive and will keep increasing as x varies from 2 to 6. Hence the function keeps increasing withing the given domain range.
So the maximum dy/dx and hence y will occur at x =6 and similarly the minimum will occur at x =2

The min value = 2(2)^2 - 4(2) +4 = 4
Max value = 2(6)^2 - 4(6) +4 = 52

Answer 2

Take the derivative of the function.
Set the derivative equal to zero and solve for X
The X values of the solutions give you the positions of maxima and minima

Answer 3

Just differentiate and put equal to zero. You'll only get a minimum though.