The tangent to a curve - Math Central

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Question from Christy, a student:

I know this question is simple but I can't figure out what I'm doing wrong.

Find the equation of the tangent line to the curve 2x^2 - y^4= 1 at the point (1,1).

Here's what I did so far:
1. f'(x)= 4x-4y^3
2. f(1)= 4(1)-4y^3
3. f(1)= -4y^3=-4
4. f(1)= y^3=1

From here it starts to look like I'm doing something wrong. Even if I use implicit differentiation I get 1. Please tell me where I'm going wrong here

Hi Christy,

You mentioned implicit differentiation and that is what you should be using. In the given expression

2x² - y⁴ - 1

think of y as a function of x and find y'. If you differentiate both sides with respect to x you get

4x - 4y³ y' = 0

x - y³ y' = 0.

Substitute for x and y at the given point (1, 1) and solve for y'. The tangent line is then the line through (1, 1) with slope y' at (1, 1).

I hope this helps,
Penny

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