Doubt from maxima and minima

Is a=4.14 ?

Can you show the solution, answer not available

Though i may be incorrect but i did first differentiate fxn w.r.tx and then i had put D=0 though i think its wrong because after first differentiation i am not able to get how to prove maxima or minima as double derivative gives it only depends on x but what about a

Sorry i did some wrong because after correction i am getting double derivative as greater than zero which is not possible so sorry ignore my working

Diffrentiate ull get the quadratic ......Now it says that Point of maxima should be positive and we know that for a cubic on moving right to left on x axis we first get minima and then maxima......hence the left sided root of the quadratic must be positive which means both roots should be positive ....Now Apply the Location of Root concept ..and get The values of a

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Is this always true?

How you deduced this?

If the leading coefficient is positive then its true