the normal line to the graph y=x^4 +1 at x=1 also intersects the graph at which of the following values of x?

Question

anonymous · Answer

slope of line you get by finding the derivative and replacing x by 1
then take the negative reciprocal to find the slope of the  normal

k?

anonymous · Answer

ok so i get -1/4, but i dont understand what to do next. do i use a graphing calc?

anonymous · Answer

???

anonymous · Answer

$$y'=4x^3$$ at 1 get 4, negative reciprocal is 
$$-\frac{1}{4}$$ so that his the slope of the normal line
at x = 1, y = 2 to the equation of the normal line is 
$$y-2=-\frac{1}{4}(x-1)$$ or 
$$y=-\frac{1}{4}(x-1)+2$$

anonymous · Answer

obviously the normal line intersects the graph at 
$$(1,2)$$ the question is where else does it intersect.

anonymous · Answer

and for that one you are on your own because you have a fourth degree equation to solve, and it is not trivial

phi · Answer

sat gave you most of the answer.  You could use a graphing calculator to finish the problem.

You have two curves:
$$ y= x^4 +1 $$
$$ y= -\frac{1}{4}x + \frac{9}{4} $$
you have to find where they intersect.