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

a) x ^2 + 2x -5

Answers (1)

f(x)  = x ^2 + 2x -5
f^{'}(x) = 2x + 2 = 2(x+1)
Now, 
f^{'}(x) = 0 \\ 2(x+1) = 0\\ x = -1

The range is from (-\infty,-1) \ and \ (-1,\infty)
In interval (-\infty,-1)   f^{'}(x)= 2(x+1) is -ve 
Hence, function f(x)  = x ^2 + 2x -5 is strictly decreasing in interval  (-\infty,-1)
In interval (-1,\infty)  f^{'}(x)= 2(x+1) is +ve
Hence, function f(x)  = x ^2 + 2x -5 is strictly increasing in interval  (-1,\infty)

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