Answer to Question #276005 in Calculus for Annah

Question

Find an equation of the tangent line to the curve x⁴ + 2y⁴ = 33 at the point (1,2).

Answer 1

$x^4+2y^4=33$

Differentiate both sides with respect to $x$

$4x^3+8y^3y'=0$

$y'=-\dfrac{x^3}{2y^3}$

Point (1,2)

$slope=m=-\dfrac{1^3}{2(2^3)}=-\dfrac{1}{16}$

The equation of the tangent line in point-slope form

$y-2=-\dfrac{1}{16}(x-1)$

The equation of the tangent line in slope-intercept form

$y=-\dfrac{1}{16}x+\dfrac{33}{16}$