Find the value(s) of a for which f(x) = x3 – ax is an increasing fun

1.	Find the value(s) of a for which f(x) = x3 – ax is an increasing function on R ?
Answer» We have, f(x) = x³ – ax f'(x) = 3x² - a Given that f(x) is on increasing function \(\therefore\) f'(x) 0 for all x ∈ R \(\Rightarrow\) 3x² - a > 0 for all x ∈ R \(\Rightarrow\) a < 3x² for all x ∈ R But the last value of 3x² = 0 for x = 0 ∴ a ≤ 0

Find the value(s) of a for which f(x) = x3 – ax is an increasing function on R ?

Answer»

We have,

f(x) = x³ – ax

f'(x) = 3x² - a

Given that f(x) is on increasing function

\(\therefore\) f'(x) 0 for all x ∈ R

\(\Rightarrow\) 3x² - a > 0 for all x ∈ R

\(\Rightarrow\) a < 3x² for all x ∈ R

But the last value of 3x² = 0 for x = 0

∴ a ≤ 0