Home
Class 12
MATHS
Let f(x)=|x^3sinxcosx6-1 0p p^2p^3|,w h...

Let `f(x)=|x^3sinxcosx6-1 0p p^2p^3|,w h e r ep` is a constant. Then `(d^3)/(dx^3)(f(x))` at `x=0` is `p` (b) `p-p^3` `p+p^3` (d) independent of `p`

A

p

B

`p + p^(2)`

C

`p + p^(3) `

D

independent of p

Text Solution

Verified by Experts

The correct Answer is:
D
Given, `f(x) = |{:(x^(3)" "sin x" "cos x),(6" "-1" "0),(p" "p^(2)" "p^(3)):}|`
On differentiating w.r.t. x, we get
`f'(x) =|{:(3x^(2)" "cos x" "-sin x),(6" "-1" "0),(p" "p^(2) " "p^(3)):}|+|{:(x^(3)" "sin x" "cos x),(0" "0" "0),(p" "p^(2)" "p^(3)):}|+|{:(x^(3) " "sin x" "cos x),(6" "-1" "0),(0" "0" "0):}|`
` rArr" "f'(x)=|{:(3x^(2)" "cos x" "-sin x),(6" "-1" "0),(p" "p^(2)" "p^(3)):}|`
`rArr" "f''(x)=|{:(6x" "-sinx" "-cos x),(6" "-1" "0),(p" "p^(2)" "p^(3)):}|+0+0`
`and f'''(x) =|{:(6" "-cos x" "sin x),(6" "-1" "0),(p" "p^(2)" "p^(3)):}|+0+0`
`:. f'''(0)=|{:(6" "-1" "0),(6" "-1" "0),(p" "p^(2)" "p^(3)):}|=0="independent of p"`
Promotional Banner

Similar Questions

Explore conceptually related problems

Let f(x)=|[x^3,sinx,cosx],[6,-1, 0],[p, p^2,p^3]|,w h e r ep is a constant. Then (d^3)/(dx^3)(f(x)) at x=0 is (a) p (b) p-p^3 (c) p+p^3 (d) independent of p

Let E and F be events with P(E) = (3)/(5), P(F)= (3)/(10) and P(EnnF)= (1)/(5) Are E and F independent?

Let E and F be events with P(E) = (3)/(5) , P(F)= (3)/(10) and P(EnnF) = (1)/(5) .Are E and F independent?

Let p(x)=x^(2)-4x+3 . Find the value of p(0),p(1),p(2),p(3) and obtain zeroes of the polynomial p(x) .

(x-3) is a factor of p(x) , if p(_) =0

Let E and F be events with P(E)=(3)/(5), P(F)=(3)/(10) and P (E cap F) =(1)/(5) Are E and F independent?

P(A)= (3)/(5) and P(B)= (1)/(3) . Find P(A and B) if A and B are independent events.

If p,q are the roots of ax^(2)-25x+c=0 , then p^(3)q^(3)+p^(2)q^(3)+p^(3)q^(2)=

If p(x)=x^(2)-5x-6 , then find the values of p(1),p(2),p(3),p(0),p(-1),p(-2),p(-3) .

( x+3) is a factor of p(x) , if p(_) =0