Question

f(x) = fourth root of x. x=16. Compute the derivative and find the equation of the tangent line

Answer 1

If I am understanding the question correctly then we can find the equation of the tangent line by finding its derivative and obtaining a point on the line.

if \[f(x)=\sqrt[4]{x}= x ^{1/4}\]
then \[f'(x) =(1/4)x ^{-3/4}\] so when x=16, f'=1/32 and \[f=\sqrt[4]{16}=2\]
So a point on the tangent line is: (16,2)
we can now solve the equation of the tangent using: \[y-y _{1}=m(x-x _{1)}\] where m is the gradient of the tangent f'
y-2=(1/32)(x-16) so y=(x/32) + 3/2

Let us know if the above is correct...

Answer 2

Thanks, it was right.

Answer 3

Cheers!