**Technifi Expert’s Answer:**

Definition of O and :

- O : The function f(n) = O(g(n)) iff there exists positive constants C and n
_{0} such that f(n) <= C*g(n) for all n > n_{0}.

Here , f(n)= 6n^{2} + 20n

6n^{2} + 20 n <= 10* n^{3} n > 1

Here , g(n) = n^{3}

C= 10, n_{0} = 1, both are positive constants.

f(n) O(n^{3})

- : A function f(n) = (g(n)) iff there exists positive constants C and n
_{0} such that f(n) >=C* g(n) n>=n_{0}

Here f(n) = 6n^{2} + 20n

6n^{2} + 20n >= n^{3} when n > 1 && n<6. But for values of n>6, this doesn’t hold true.

Here g(n) = n^{3}

C=1

f(n) (n^{3}) .

Whereas, 6n^{2} + 20n > 6n^{2} , n>1

Here g(n) = n^{2}

C = 6 and n_{0} = 1.

f(n) (n^{2})

Therefore, 6n^{2} + 20n = O(n^{3}) but 6n^{2} + 20n (n^{3}) .

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