Question

The equation of the tangent line at an inflection point of $f\left(x\right)=x^4-6x^3+12x^2-8x+3$ is

• A. y$=3x+4$
• B. y$=4$
• C. y$=3x+2$
• D. none of these

Answer 1

The correct option is D none of these

Given, $f\left(x\right)=x^4-6x^3+12x^2-8x+3$
At inflection point $f^{\prime \prime }\left(x\right)=0$
$12x^2-36x+24=0$
$(x-2)(x-1)=0$
$x=2,1$
$f^{\prime }\left(x\right)=4x^3-18x^2+24x-8$
$f^{\prime }\left(1\right)=2$ and $f^{\prime }\left(2\right)=0$
$f\left(1\right)=2$ and $f\left(2\right)=3$
So the equations are $y=3$ and $y=2x$