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tangent f(x)=3x^4-8x^2,(-1,5)

解答

切线

f (x) = 3 x^{4} - 8 x^{2}, (- 1, 5)

解答

y = - 4.38103 \dots x + 0.61896 \dots or y = - 5.01374 \dots x - 0.01374 \dots

求解步骤

(- 1, 5)

处的切线斜率:

m = \frac{3 x ^{4} - 8 x ^{2} - 5}{x + 1}

计算

f (x) = 3 x^{4} - 8 x^{2}

的斜率:

m = 12 x^{3} - 16 x

解

12 x^{3} - 16 x = \frac{3 x ^{4} - 8 x ^{2} - 5}{x + 1} : x \approx 0.29260 \dots, x \approx 0.94371 \dots

求出

x = 0.29260 \dots

处的切线:

y = - 4.38103 \dots x + 0.61896 \dots

求出

x = 0.94371 \dots

处的切线:

y = - 5.01374 \dots x - 0.01374 \dots

y = - 4.38103 \dots x + 0.61896 \dots or y = - 5.01374 \dots x - 0.01374 \dots

作图

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