If p(x) is a polynomial of degree 3 which sat | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let $p(x) = ax^3 + bx^2 + cx + d$ be a polynomial of degree $3$.Then,the derivatives are:$p^{\prime}(x) = 3ax^2 + 2bx + c$$p^{\prime \prime}(x) =

Vedclass · Accepted Answer

$-6$

Vedclass · Answer

(B) Let $p(x) = ax^3 + bx^2 + cx + d$ be a polynomial of degree $3$.Then,the derivatives are:$p^{\prime}(x) = 3ax^2 + 2bx + c$$p^{\prime \prime}(x) = 6ax + 2b$$p^{\prime \prime \prime}(x) = 6a$Given $p^{\prime \prime \prime}(1) = 6$,we have $6a = 6$,which implies $a = 1$.Given $p^{\prime \prime}(1) = 0$,we substitute $a = 1$ into $p^{\prime \prime}(1) = 6a(1) + 2b = 0$:$6(1) + 2b = 0 \Rightarrow 2b = -6 \Rightarrow b = -3$.Now,we need to find $p^{\prime \prime}(0)$:$p^{\prime \prime}(0) = 6a(0) + 2b = 2b$.Substituting $b = -3$,we get $p^{\prime \prime}(0) = 2(-3) = -6$.

If $p(x)$ is a polynomial of degree $3$ which satisfies $p^{\prime \prime}(1)=0$ and $p^{\prime \prime \prime}(1)=6$,then $p^{\prime \prime}(0)$ is equal to

Similar Questions

$f(x) = e^x \sin x$,then $f^{(6)}(x)$ is equal to :

If $y = A \cos nx + B \sin nx$,then $\frac{d^2 y}{dx^2} = $

If $y=500 e^{7 x}+600 e^{-7 x},$ show that $\frac{d^{2} y}{d x^{2}}=49 y$.

If $y = \cos^{-1} x$,find $\frac{d^{2} y}{d x^{2}}$ in terms of $y$ alone.

If $y=(\tan^{-1} x)^{2}$,show that $(x^{2}+1)^{2} y_{2}+2 x(x^{2}+1) y_{1}=2$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module