Question

ff 5x2 + y4 = 21 then evaluate the second derivative of y with respect to x when x = 2 and y = 1. Round your answer to two decimal places. Use the hyphen symbol, -, for negative values. PLEASE ANSWER ASAP

Answer 1

It is given that ,
`5 x^(2)  + y ^(4)= 21\\\\y^(4)= 21 - 5 x^(2)`

Differentiating both sides with respect to x, we get

→4 y³ y' = 0 - 10 x , where y' is first derivative of y w.r.t x.

→4 y³ y' = - 10 x

When x=2, y=1, substituting these values in above equation

→4× 1³×y'= -10×2

→ y'= -20/4= -5

Differentiating again w.r.t x,the above equation we get

→4 [ 3 y²y'² + y³ y''] = -10 where y'' is double derivative of y w.r.t x.

→3 y²y'² + y³ y'' = -10/4= -5/2

Substituting x=2, y=1, y'= -5,in above equation we get

→ 3 ×1²×(-5)² + 1³× y'' = -5/2

→ 75 + y'' = -5/2

→ y''= -5/2 - 75

→ y'' =
`(-150-5)/(2)=(-155)/(2)= -77.50`

→ y''= -77.50(Answer)