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 Need solution for RD Sharma maths class 17 chapter Maxima and Minima  exercise 17.1 question 6

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Minimum value and maximum value does not exist.


f(x) have max value in [a, b] such that f(x) ≤ f(c) for all x belongs to [a ,b] and if f(x) ≥ f(c) then f(x) has minimum value.


f(x)=2 x^{3}+5 \text { on } R


We have,

f(x)=2 x^{3}+5 \text { on } R

We know,

f(x) increase when value of x is increases

In this case, the value of f(x) increases rapidly, so it does not attain maximum value.

Also, f(x) can be made as small as possible. So it does not attain minimum value.

Hence, given function does not have maximum value and minimum value.

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