Determine an equation of the line tangent to the graph of the following equation at the indicated point: f(x) = (9x^2 +64)^1/2 ;(2,10). I think my first step is to find the derivative however what do I do with the ^1/2 part?

Question

anonymous · Answer

The derivative of your equation will give you the slope of the tangent line which will be given by:$$y-f(a)=f'(a)(x-a)$$Where (x,f(a))=(2,10)

anonymous · Answer

the derevative is 9x/2($$(\sqrt{9x^2+64})$$

anonymous · Answer

First find the derivative:$$f'(x)=\frac{18x}{(9x^2+64)^{1/2}}$$And,$$f'(2)=\frac{18(2)}{[9(2)^2+64]^{1/2}}=\frac{36}{100^{1/2}}=(18/5)$$So you tangent line is given by:$$y-10=3.6(x-2)$$Or,$$y=(18/5)x+(14/5)$$

anonymous · Answer

I meant to leave 3.6 as a fraction above.  i.e.,: 3.6=18/5 I didnt mean to switch from decimals to fractions mid thread lol

anonymous · Answer

My first response should also read (a,f(a))=(2,10) ooops

anonymous · Answer

Thank you for your help!

anonymous · Answer

@ eseidl ur f' is wrong

anonymous · Answer

I wondered about that. When I plugged in 2 in the f'(x) I got 180 not 18/5

anonymous · Answer

9x/2(9x^2+64)^1/2 is correct