The function, f x = 3 x - 7 x 2 3 ,   x ∈ R , is increasing for all x lying in

Question

The function, f x = 3 x - 7 x 2 3 , &#160; x &#8712; R , is increasing for all x lying in

Aicharya · Accepted Answer

f x = 3 x - 7 x 2 3 For f x is increasing f ' x &#62; 0 . Differentiate f x f ' x = 3 x 2 3 + 3 x - 7 2 3 x 1 3 f ' x = 9 x + 2 3 x - 7 3 x 1 3 f ' x = 15 x - 14 3 x 1 3 Now f ' x &#62; 0 &#160; &#160; &#8658; 15 x - 14 3 x 1 3 &#62; 0 x &#8712; - &#8734; , &#160; 0 &#8746; 14 15 , &#160; &#8734;

The function, f x = 3 x - 7 x 2 3 , &#160; x &#8712; R , is increasing for all x lying in

Solution

The function, f x = 3 x - 7 x 2 3 , x ∈ R , is increasing for all x lying in