Answer:
The interval which contains the local minimum is [2.5 , 4] ⇒ last answer
Step-by-step explanation:
"I have added screenshot of the complete question as well as the diagram"
- From the graph of the function there are two local minimum points
- Point (-0.44 , -4.3) and point (3 , -4)
- At the the minimum local points the differentiation of the function
equal to zero
- If the the name of the function on the graph is h(x)
∵ h'(x) = 0 gives two values of x, one of them is -0.44 and the other is 3
∴ h'(-0.44) = 0
∴ h'(3) = 0
- The interval which contains the local minimum must has on of
these two values -0.44 and 3
∵ x = -0.44 is between -1 and 0
∴ The interval [-4 , -2.5] does not contain local minimum
∴ The interval [-2 , -1] does not contain the local minimum
∵ x = 3 is between 2 and 4
∴ The interval [1 , 2] does not contain the local minimum
∴ The interval [2.5 , 4] contains the local minimum
* The interval which contains the local minimum is [2.5 , 4]
