Original
Find the average rate of change of {{MATH_9}} on the interval {{MATH_10}}.
{{MATH_11}}
{{CMD_12}}
Choose the correct statement.
{{CMD_13}}
{{CMD_14}}There exists a point {{MATH_15}} in {{MATH_16}} such that the instantaneous rate of change of {{MATH_17}} at the point {{MATH_18}} is equal to the average rate of change of {{MATH_19}} on {{MATH_20}} , although the function {{MATH_21}} does not satisfy the conditions of the Mean value theorem on {{MATH_22}}.{{CMD_23}}
{{CMD_24}}There exists a point {{MATH_25}} in {{MATH_26}} such that the instantaneous rate of change of {{MATH_27}} at the point {{MATH_28}} is equal to the average rate of change of {{MATH_29}} on {{MATH_30}}, since the function {{MATH_31}} satisfies the conditions of the Mean value theorem on {{MATH_32}}.{{CMD_33}}
{{CMD_34}}There exists a point {{MATH_35}} in {{MATH_36}} such that the instantaneous rate of change of {{MATH_37}} at the point {{MATH_38}} is equal to the average rate of change of {{MATH_39}} on {{MATH_40}}, but we don't have enough information to find such a point.{{CMD_41}}
{{CMD_42}}There exists no point {{MATH_43}} in {{MATH_44}} such that the instantaneous rate of change of {{MATH_45}} at the point {{MATH_46}} is equal to the average rate of change of {{MATH_47}} on {{MATH_48}}.{{CMD_49}}
{{CMD_50}}