How do use the first derivative test to determine the local extrema #x^2-2x-3#?
There is a minima of f(x) at x= 1
Since f(x) is defined for all values of x, the only critical point is given by 2x-2=0, or, x=1
Since divide the entire domain in two parts
Now consider any value of x in
At x=-1, the slope is 0
At any point in #(1, +oo), say x=2, f'(x) would be 4-2=2. This means the slope of the curve is positive.
The above analysis of the slope of f(x) , shows that the slope of the curve changes from negative, to the left of x=1, to positive to its right. This implies that there is a minima at x=1