Answer :

Given:- Function f(x) = 10 – 6x – 2x2


Theorem:- Let f be a differentiable real function defined on an open interval (a, b).


(i) If f’(x) > 0 for all , then f(x) is increasing on (a, b)


(ii) If f’(x) < 0 for all , then f(x) is decreasing on (a, b)


Algorithm:-


(i) Obtain the function and put it equal to f(x)


(ii) Find f’(x)


(iii) Put f’(x) > 0 and solve this inequation.


For the value of x obtained in (ii) f(x) is increasing and for remaining points in its domain, it is decreasing.


Here we have,


f(x) = 10 – 6x – 2x2



f’(x) = –6 – 4x


For f(x) to be increasing, we must have


f’(x) > 0


–6 –4x > 0


–4x > 6





Thus f(x) is increasing on the interval


Again, For f(x) to be increasing, we must have


f’(x) < 0


–6 –4x < 0


–4x < 6





Thus f(x) is decreasing on interval


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