Looks fine! To determine if you're dealing with a minimum or maximum you can also make a sign table.
Can somebody tell me if my solution is correct?
Find the stationary values, determine their nature, and find the point of inflection.
Min= (2, -1)
Point of inflection= (1/2, 5.75)
At stationary points dy/dx (slope=0)
solve quadratic to find x values
Substitute into expression for y gives corresponding y values of (-1,12.5)
The second derivative=6x-3
The second derivative for x=2 =9 which is greater than 0 so this is the minimum point
The second derivative for x=-1 =-9 which is less than 0 so this is the maximum point
At the point of inflection the second derivative=0
d2y/dx2=0=6x-3 therefore x=1/2
Substituting x=1/2 into the expression for y gives y value of 5.75.
Therefore the point of inflection= (1/2, 5.75)