If f(x)=3 x^2+2 x f^{prime}(1)+f^{prime prime | vedclass

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

Question

(C) Given $f(x) = 3x^2 + 2x f'(1) + f''(2)$.Let $f'(1) = a$ and $f''(2) = b$.Then $f(x) = 3x^2 + 2ax + b$.Differentiating with respect to $x$,we get $

Vedclass · Accepted Answer

$3 x^2-12 x+6$

Vedclass · Answer

(C) Given $f(x) = 3x^2 + 2x f'(1) + f''(2)$.Let $f'(1) = a$ and $f''(2) = b$.Then $f(x) = 3x^2 + 2ax + b$.Differentiating with respect to $x$,we get $f'(x) = 6x + 2a$.At $x = 1$,$f'(1) = 6(1) + 2a = 6 + 2a$.Since $f'(1) = a$,we have $a = 6 + 2a$,which implies $a = -6$.Now,differentiating $f'(x) = 6x + 2a$ again,we get $f''(x) = 6$.Thus,$f''(2) = 6$.Since $f''(2) = b$,we have $b = 6$.Substituting $a = -6$ and $b = 6$ into the expression for $f(x)$:$f(x) = 3x^2 + 2(-6)x + 6 = 3x^2 - 12x + 6$.

If $f(x)=3 x^2+2 x f^{\prime}(1)+f^{\prime \prime}(2)$,then $f(x)=$ . . . . . .

Similar Questions

If $2 f(x)-3 f\left(\frac{1}{x}\right)=x+1$,then $f^{\prime}(\sqrt{3})$ is equal to

$x = \frac{1-\sqrt{y}}{1+\sqrt{y}} \Rightarrow \frac{dy}{dx}$ is equal to

If $y = \frac{e^x \log x}{x^2}$,then $\frac{dy}{dx} =$

Let $g(x) \neq 0, g^{\prime}(x) \neq 0, f(x) \neq 0, f^{\prime}(x) \neq 0$. If $F(x)=f(x) g(x)$,$G(x)=f^{\prime}(x) g^{\prime}(x)$,$F^{\prime}(x)=G(x) H(x)$,and $F^{\prime}(x)=F(x) K(x)$,then $H(x)+K(x)=$

If $f(x) = \frac{x}{1 + |x|}$ for $x \in R$,then $f'(0) = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module