Help with Math: Calculate Manually, No MATLAB Needed

[ann777]

Can someone help me with this? You don't need to do MATLAB, just compute manually.

 

[HOI]

Have you calculated T(x)? You are given $y^4+ xy= 2x^2- 7x+ 7$. Differentiating, $4y^3\frac{dy}{dx}+ y+ x\frac{dy}{dx}= 4x- 7$. $4y^3\frac{dy}{dx}+ x\frac{dy}{dx}= (4y^3+ x)\frac{dy}{dx}= 4x- y- 7$. $\frac{dy}{dx}= \frac{4x- y- 7}{4y^3+ x}$. At (1, 1), $\frac{dy}{dx}= \frac{4- 1- 7}{4+ 1}= \frac{-4}{5}$. $T(x)= -\frac{4}{5}(x- 1)+ 1= -\frac{4}{5}x+ \frac{1}{5}$.