Question
Find the value of a for which the function f (x) = x3 – 2ax + 6 is increasing for x > 0.
Solution
Here f (x) = x2 – 2ax – 6
∴ f ' (x) = 2x – 2a
f (x) is increasing when f ' (x) > 0
⇒ 2 (x – a) > 0 ⇒ x – > 0
⇒ x > a
But x > 0
∴ a ∊ (– ∞ , 0)
