Question

Which interval contains a local minimum for the graphed function?

Answer 1

Answer : Option D is correct i.e [2.5,4]

Explanation :

Suppose our function is f(x)

then the value of f(x) is minimum where

it reaches -0.44 and 3 with two different intervals .

As we know that for finding the local minimum ,

the criteria is that  f'(x)=0 .

So, here

f'(-0.44)=0 and

f'(3)=0

both are the local minimum point for the function f(x)

but -0.44 is the global minimum point .

In our case for [2.5,4] is the required interval where f(x) reaches its  local minimum.

Answer 2

Answer:

The correct option is D. The interval [2.5, 4] contains a local minimum for the graphed function

Step-by-step explanation:

According to the definition of local mimima, a function has local minima at c if

$f(c)$

for all values of x. where, $x\in [c-\epsilon, c+\epsilon]$

From the graph it is clear that the given function has local minima at (-0.44,-4.3) and (3,-4).

$-0.44\notin [-4, -2.5], 3\notin [-4, -2.5]$

Therefore option A is incorrect.

$-0.44\notin [-2, -1], 3)\notin [-2, -1]$

Therefore option B is incorrect.

$-0.44\notin [1, 2], 3\notin [1, 2]$

Therefore option C is incorrect.

$-0.44\notin [2.5, 4], 3\in [2.5, 4]$

Therefore option D is correct.