Let ' \( a \) ' be a real number such that the function \( f(x)=a x...

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Let ' \( a \) ' be a real number such that the function \( f(x)=a x^{2}+6 x-15, x \in R \) is increasing in \( \left(-\infty, \frac{3}{4}\right) \)
P
W and decreasing in \( \left(\frac{3}{4}, \infty\right) \). Then the function \( g(x)=a x^{2}-6 x+15, x \in R \) has a:
[JEE Main-2021]
(a) local maximum at \( x=-\frac{3}{4} \)
(b) local minimum at \( x=-\frac{3}{4} \)
(c) local maximum at \( x=\frac{3}{4} \)
(d) local minimum at \( x=\frac{3}{4} \)
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