Let 'a' be a real number such that the function f(x) = ax2 + 6x $-$ 15, x $\in$ R is increasing in $\left( { - \infty ,{3 \over 4}} \right)$ and decreasing in $\left( {{3 \over 4},\infty } \right)$. Then the function g(x) = ax2 $-$ 6x + 15, x$\in$R has a :

Question

Let 'a' be a real number such that the function f(x) = ax² + 6x $-$ 15, x $\in$ R is increasing in $\left( { - \infty ,{3 \over 4}} \right)$ and decreasing in $\left( {{3 \over 4},\infty } \right)$. Then the function g(x) = ax² $-$ 6x + 15, x$\in$R has a :

local maximum at x = $-$ ${{3 \over 4}}$

local minimum at x = $-$${{3 \over 4}}$

local maximum at x = ${{3 \over 4}}$

local minimum at x = ${{3 \over 4}}$

Solution

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