val186
12.08.2021 •
Mathematics
Differentiate 4x^2+y^2=36 with respect to x. Hence find the turning points of the curve.
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Ответ:
If y = y(x), then the derivative with respect to x is dy/dx. Differentiating both sides of the given equation gives
d/dx [4x ² + y ²] = d/dx [36]
8x + 2y dy/dx = 0
2y dy/dx = -8x
dy/dx = -4x/y
The turning points of the curve, taken as a function of x, are those points where the derivative vanishes.
-4x/y = 0 ===> x = 0
This value of x corresponds to two points on the curve,
4×0² + y ² = 36 ===> y ² = 36 ===> y = ±6
So there are two turning points, (0, -6) and (0, 6).
Ответ:
9x⁴ - x²y² - 5y⁴ - 3x⁴ - 2x²y² + 7y⁴
6x⁴ - 3x²y² + 2y⁴