Question

Let f(x) = `|(x^2, sin x),(p, -1)|,` where p is a constant. The value of p for which f'(0) = 1 is ______.

विकल्प

• `RR`

• 1

• 0

• −1

Answer 1

Let f(x) = `|(x^2, sin x),(p, -1)|,` where p is a constant. The value of p for which f'(0) = 1 is -1.

Explanation:

Given f(x) = `|(x^2, sin x),(p, -1)|`

⇒ f(x) = −x² − p sin x

⇒ f'(x) = −2x − p cos x

Also, given that f' (0) = 1

⇒ −2(0) − p(cos 0) = 1

⇒ −p = 1 

⇒ p = −1