find an equation of the tangent line at point given: f(x)=8/x^2+4; (2,1)

Question

myininaya · Answer

Have you differentiated f yet?

anonymous · Answer

not sure how

anonymous · Answer

would i have to plug in the point into the point slope form ? or

myininaya · Answer

$$f(x)=\frac{8}{x^2+4} \text{ or } f(x)=\frac{8}{x^2}+4 ?$$

myininaya · Answer

I think you mean the first one because (2,1) isn't on the second graph

myininaya · Answer

To differentiate f you need to know the quotient rule

myininaya · Answer

Or at least the product rule and chain rule

anonymous · Answer

yeah the first one

myininaya · Answer

Do you know the quotient rule?

anonymous · Answer

f'g-fg'/g^2 ?

myininaya · Answer

$$f'(x)=\frac{(8)'(x^2+4)-8(x^2+4)'}{(x^2+4)^2}$$

myininaya · Answer

so you need to know the derivative of 8 and the derivative of x^2+4 to finish that

anonymous · Answer

okie dokie !

myininaya · Answer

once you are done with that replace the x's with 2'
to find f'(2) this will be the slope of the tangent line of f at (2,1)

myininaya · Answer

then once you know the slope that is it plug in the point-slope form of a line 
y-y1=m(x-x1)

myininaya · Answer

$$y-1=m(x-2)$$

myininaya · Answer

your only job is to find m
which is f'(2)