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

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