What are the absolute extrema of #f(x)=2x^2 - 8x + 6 in[0,4]#?
Absolute extrema (the min. and max. values of a function over an interval) can be found by evaluating the endpoints of the interval and the points where the derivative of the function equals 0.
We begin by evaluating the endpoints of the interval; in our case, that means finding
Next, find the derivative:
And find the critical points; i.e. the values for which
Evaluate the critical points (we only have one,
Finally, determine the extrema. We see that we have a maximum at