Question

Let f(x) = tan^-1x. Then f'(x) + f"(x) is equal to 0, when x is equal to ______ 

पर्याय

• 0

• 1

• i

• -i

Answer 1

Let f(x) = tan^-1x. Then f'(x) + f"(x) is equal to 0, when x is equal to 1.

Explanation:

f(x) = tan^-1x

∴ f'(x) = `1/(1 + x^2)`

∴ f''(x) = `(-1)/(1 + x^2)^2 . 2x`

Since f'(x) + f"(x) = 0

∴ `1/(1 + x^2) - (2x)/(1 + x^2)^2 = 0`

⇒ 1 + x² - 2x = 0

⇒ x = 1