The Equation of the normal line to the curve Y=X^4+3X^3+2 at the point where X=0 is..

[jiwon28874]

The Equation of the normal line to the curve Y=X^4+3X^3+2 at the point where X=0 is...
a) y=x
b) y=13x
c) y=0
d) y=x+2
e) x=0

My teacher says the answer is E but I do not know why.
PLEASE HELP!

 

[pka]

The Equation of the normal line to the curve Y=X^4+3X^3+2 at the point where X=0 is...
a) y=x b) y=13x c) y=0 d) y=x+2 e) x=0
My teacher says the answer is E but I do not know why.

If you look at the graph, that answer is clearly correct.

 

[jiwon28874]

RE:

Hi,
but this is a non-calculator problem.
How can you do this by taking the derivative and finding the equation of the normal line?

 

[pka]

Hi,
but this is a non-calculator problem.
How can you do this by taking the derivative and finding the equation of the normal line?

The tangent line at \(\displaystyle (0,2)\) has slope \(\displaystyle 0\) so the normal line has an undefined slope. That means the equation is \(\displaystyle x=0\).