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+1 vote
13.6k views
in Mathematics by (49.6k points)

Find the intervals in which the function f given by f(x) = x2 – 4x + 6 is strictly increasing.

1 Answer

+2 votes
by (49.6k points)
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Best answer

f(x) = x2 - 4x + 6 

f1 (x) = 2x - 4 

f1 (x ) = 0 given, 2x - 4 = 0 

⇒ 2x =4 

⇒ x = 2 

Thus f1(x ) = 0 at x = 2 

Now, the point x = 2 divides the real line into two disjoint intervals namely, 

(-∞,2) and (2,∞). 

At (2,∞),f1 (x) > 0 

⇒ f is strictly increasing at(2,∞)

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