Question

find an equation for the tangent and normal line to the curve 2x^2 + (1/x^4) when x=1

Answer 1

\[
f(x) = 2x^2 + \frac{1}{x^4} \\
\text{when x = 1:} \\
f(1) = 2*1 + \frac 11 = 3 \\
(1,3) \text{ is a point on the curve.}\\
\text{To find the equation of the tangent through (1,3) find the slope.}\\
\text{Find f '(x) and then f '(1) which will be the slope of the tangent at x = 1}\\
m = f'(1) = ? \\
\text{Equation of tangent through (1,3) is: } y - 3 = m(x - 1)
\]