Tag: functions and graphs

If $y^2 = ax^2 +bx+c$, then $y^2 \dfrac{d^2y}{dx^2}$ is

If $fxln\left(1+\dfrac{1}{x}\right)dx=p(x)ln\left(1+\dfrac{1}{x}\right)+\dfrac{1}{2}x-\dfrac{1}{2}ln(1+x)+c$, being arbitary costant, then

Let $f(x)$ is cubic polynomial with real coefficient such that $f''(3) = 0, f'(5) = 0$. If $f(3) = 1$ and $f(5) = -3$, then $f(1)$ is equal to

$f (x) = x^4 - 10x^3 + 35x^2 - 50x + c$ is a constant. the number of real roots of . f (x) = 0 and 
f'' (x) = 0 are respectively 

The positive integers $x$ for which $f(x)=x^{3}-8x^{2}+20x-13$ is a prime is

If $f\quad \left( x \right) ={ x }^{ 2 }+2bx+{ 2c }^{ 2 }\quad and\quad g\quad (x)\quad ={ -x }^{ 2 }\quad -2cx+{ b }^{ 2 }\quad are\quad such\quad that\quad min\quad f\quad (x)\quad >\quad max\quad g\quad (x),\quad then$ relation between b and c, is

If $f(x)$ is a polynomial function satisfying $f(x)f\left(\dfrac{1}{x}\right)=f(x)+\left(\dfrac{1}{x}\right)$ and $f(3)=28$, then $f(4)=$

If $f\left(x\right)$ is a polynomial such that $ f\left(a\right) f\left(b\right)<0$, then number of zeros lieing between $a$ and $b$ is 

If $ P ( X ) = x ^ { 3 } - 3 x ^ { 2 } + 2 x + 5 $ and P ( a ) = P ( b ) = P ( c ) = 0 then the value of ( 2 - a ) ( 2 - b ) ( 2 - c ) is

If f : R $\rightarrow$ R, g : R $\rightarrow$ R and h : R $\rightarrow$ R is such that $f(x) = x^2, g(x) = tan  x$ and $h(x) = log  x$, then the value of [ho(gof)], if $x = \displaystyle \dfrac{\pi}{2}$ will be