Which interval contains a local minimum for the graphed function?A.) [-4, -2.5]B.) [-2, -1]C.) [1, 2]D.) [2.5, 4]

Accepted Solution

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)=0both 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.