Question

Find an equation of the tangent line to the curve at the given point x^(1/4)

Answer 1

\[y(x)=x^{\frac{1}{4}}\]

\[y'(x)=\frac{1}{4}x^{\frac{1}{4}-\frac{4}{4}}\]
\[y'(x)=\frac{1}{4}x^{\frac{-3}{4}}\]

Answer 2

ytan = mx + b, tangent line
y = x^(1/4), original
m = y' = (1/4)x^(-3/4)
b is determined by given point

ytan = (1/4)x^(-3/4)*x + b
= x^(1/4 - 3/4) + b
= x^(-2/4) + b
= x^(-1/2) + b

Ans x^(-1/2) + b