The number of points, where the curve y = x 5 - 20 x 3 + 50 x + 2 crosses the x -axis, is _____.

Step-by-step solution

Let, f ( x ) = x 5 - 20 x 3 + 50 x + 2 Now differentiating the function f x with respect to x we get, f ' ( x ) = 5 x 4 - 60 x 2 + 50 ⇒ f ' ( x ) = 5 x 4 - 12 x 2 + 10 Now equating f ' ( x ) = 0 we get, x 4 - 12 x 2 + 10 = 0 ⇒ x 2 = 12 ± 144 - 40 2 ⇒ x 2 = 6 ± 26 ⇒ x 2 ≈ 11 . 1 ,   0 . 9 ⇒ x ≈ ± 3 . 31 ,   ± 0 . 95 Now finding the nature of function at integer value near by above value we get, f 0 = 2 ,   f 1 > 0 ,   f