Question

Determine the location of the vertex and determine the nature of the vertex for the graphs of: y = x^3 - 6x^2 -15x + 7

Answer 1

(5, -93) local minima, (-1, 15) local maxima

Explanation:

differentiate this equation, we get

y' = 3x^2 - 12 x -15

the x-axis of the vertices are:

3x^2 - 12x - 15 = 0

(x-5)(3x+3) = 0

x1 = 5 and x2=-1

so the positions of the vertices are (5, -93) and (-1 , 15)

(5, -93) is the local minima, and (-1, 15) is the local maxima