Question

Which statement correctly identifies a local minimum of the graphed function?

A. Over the interval [–3, –2], the local minimum is 0.
B. Over the interval [–2, –1], the local minimum is 2.2.
C. Over the interval [–1, 0.5], the local minimum is 1.
D. Over the interval [0.5, 2], the local minimum is 4.

Answer 1

That would be option C.

Answer 2

C. Over the interval [–1, 0.5], the local minimum is 1.

Explanation:

From the graph we observe the following:

1) x intercepts are two points.

ii) y intercept = 1

f(x) = y increases from x=-infinity to -1.3

y decreases from x=-1.3 to 0

Again y increases from x=0 to end of graph.

Hence in the interval for x as (-1.3, 1) f(x) has a minimum value of (0,1)

i.e. there is a minimum value of 1 when x =0

Since [-1,0.5] interval contains the minimum value 1 we find that

Option C is right answer.

There is a local minimum of 1 in the interval [-1,0.5]