Finding local maxima and minima of a function given the graph

Question

Here is a graph of the function g

.

Use the graph to find the following.

If there is more than one answer, separate them with commas.

A. All local minimum values of g;

B. All values at which g has a local minimum

Answer 1

g(-2) = -4 = the local minimum and the global minimum

just one local minimum, just one global minimum when x =-2

g(x) is an upward opening parabola with x intercepts -4 and 0, y intercept=0

g(x) = y = (x+4)(x+0) = x^2+4x

the vertex of the parabola is (-2,-4)

other points on the graph are (1,5) and (-5,5)

axis of symmetry is x=-2

y = (x+2)^2 -4 = x^2+4x

to find the local minimum, set the derivative = 0

y' = 2x+4 = 0

x =-4/2 = -2 = the x value for the minimum g(x)

y(-2) =g(-2) = (-2)^2 +4(-2) = 4-8 = -4 = the local (and global) minimum g(x)

A. -4

B. -2