f(x)=(x^2)+1+(1/(x^4)), c=1; (a) find the slope of the line that is tangent to the graph of f(x) at the given point x=c; (b) write an equation of the tangent line to the graph of f(x) at the point (c,f(c))

Question

misty1212 · Answer

HI!!

misty1212 · Answer

$$f(x)=x^2+1+\frac{1}{x^4}$$?

clara1223 · Answer

yep!

misty1212 · Answer

do you know the derivative?

misty1212 · Answer

lol another county heard from 
you got $f'(x)$ 
if not let me know

clara1223 · Answer

I get that the derivative is 2x-(4/(x^5))

clara1223 · Answer

yeah this is calc

misty1212 · Answer

ok looks good
plug in 1 what do you get?

clara1223 · Answer

-2

misty1212 · Answer

ok so $m=-2$ 
next i guess find $f(1)$

misty1212 · Answer

oh, the answer to question 1 was $-2$ 
now we can find the equation of the tangent line, once we have the point

clara1223 · Answer

how do you construct the equation of the tangent line? I know in class we use y-y1=m(x-x1) and that m=f'(c) but what are y1 and x1?

anonymous · Answer

$$x_1=1,y_1=f(1)$$

clara1223 · Answer

Oh! duh! (c,f(c)). the question told me that. thanks!!