Answer:
(-1, 0)
Explanation:
Jim, please use the symbol " ^ " to indicate exponentiation:
y = x^3 + 3x^2 – x – 3. Thanks.
A "turning point" is a point on the graph of a function at which the derivative changes sign (e. g., from positive to negative or vice versa). To identify turning points, we differentiate the given function twice, set the second derivative equal to zero and identify the x-values at which the sign of the derivative changes.
Given y = x^3 + 3x^2 – x – 3,
dy/dx = 3x^2 + 6x - 1
d²y
------ = 6x + 6 and this is zero at x = -1.
dx²
We can easily show that the 2nd derivative changes sign at x = -1.
Thus, the only turning point here is (-1, [-1]³ + 3[-1]² - [-1] - 3), or (-1, 0).