Question

An equation of the tangent to the curve $y=x^4$ from the point $(2,0)$ not on the curve is:

• A. $y=0$
• B. $x=0$
• C. $x+y=0$
• D. $noneofthese$

Answer 1

The correct option is A $y=0$

let a,b be point on curve (x, y)

$b=a^4$

$\frac{dy}{dx}\left(x^4\right)=4x^3=4a^3$

$(y-y_1)=m(x-x_1)\to$ be tangent equation passes through (2, 0)

$(b-0)=4a^3(a-2)$

$a^4=4a^3(a-2)$

$3a^4-8a^3=0$

$a^3(3a-8)=0$

$a=0ora=\frac{8}{3}(0,0)$ & $[\frac{8}{3},{\left(\frac{8}{3}\right)}^4]$ points on curve

$b=0orb={\left(\frac{8}{3}\right)}^4$

$(y-0)=\frac{0-0}{2-0}(x-0)\Rightarrow y=0\to$tangent (1)

$[y-{\left(\frac{8}{3}\right)}^4]=\frac{(\frac{8}{3}{)}_{-0}^4}{(\frac{8}{3}{)}_{-2}}(x-\frac{8}{3})\to$tangent (2)