Find the intervals in which the function f given by f(x) = x2 – 4x +

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

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

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

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