Prove that the following function is increasing on r?
i. f(x) = 3x⁵ + 40x³ + 240x

ii. f(x) = 4x³ – 18x² + 27x – 27

Question

Prove that the following function is increasing on r? i. f(x) = 3x 5 + 40x 3 + 240x ii. f(x) = 4x 3 – 18x 2 + 27x – 27

Philoid · Accepted Answer

(i) we have

f(x) = 3x⁵ + 40x³ + 240x

Now,

xR

Hence, f(x) is an increasing function for all x

(ii) we have

f(x) = 4x³ – 18x² + 27x – 27

Now,

x R

Hence, f(x) is an increasing fuction for all x

Prove that the following function is increasing on r?i. f(x) = 3x5 + 40x3 + 240xii. f(x) = 4x3 – 18x2 + 27x – 27