Question
The image of the interval $$\left[ {1,\,3} \right]$$ under the mapping $$f:R \to R,$$ given by $$f\left( x \right) = 2{x^3} - 24x + 107$$ is :
A.
$$\left[ {0,\,89} \right]$$
B.
$$\left[ {75,\,89} \right]$$
C.
$$\left[ {0,\,75} \right]$$
D.
none of these
Answer :
$$\left[ {75,\,89} \right]$$
Solution :
Since, the given function has minimum value 75 which is attained at $$x = 2$$ and maximum value 89 which is attained at $$x = 3.$$ Hence, the range of $$f$$ is $$\left[ {75,\,89} \right].$$