The Total solution for NCERT class 6-12
Show that f(x) = x3 –15x2 + 75x – 50 is an increasing function for allx ϵ R.
Given f(x) = x3 – 15x2 + 75x –50
⇒
⇒ f’(x)= 3x2 – 30x + 75
⇒ f’(x)= 3(x2 – 10x + 25)
⇒ f’(x)= 3(x – 5)2
Now, as given x ϵ R
⇒ (x– 5)2 > 0
⇒ 3(x– 5)2 > 0
⇒ f’(x)> 0
Hence, condition for f(x) to be increasing
Thus f(x) is increasing on interval x ∈ R