6) Find the intervals in which the following functions are strictly increasing or
decreasing:

d) 6- 9x - x ^2

Answers (1)

Given function is,
f(x) = 6- 9x - x ^2
f^{'}(x) = - 9 - 2x
Now,
f^{'}(x) = 0\\ - 9 - 2x = 0 \\ 2x = -9\\ x = -\frac{9}{2}

So, the range is  (-\infty, - \frac{9}{2} ) \ and \ ( - \frac{9}{2}, \infty )
In interval (-\infty, - \frac{9}{2} ) ,  f^{'}(x) = - 9 - 2x  is +ve
Hence,  f(x) = 6- 9x - x ^2  is strictly increasing in interval  (-\infty, - \frac{9}{2} )
In interval ( - \frac{9}{2},\infty ) , f^{'}(x) = - 9 - 2x is -ve
Hence,  f(x) = 6- 9x - x ^2  is strictly decreasing in interval ( - \frac{9}{2},\infty )

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