%%

6. 函数 $f(x)=x^{4}-2 x^{3}$ 的图像在点 $(1, f(1))$ 处的切线方程为 ()

Gaokao · Math · previous-year question

  1. A.$y=-2 x-1$
  2. B.$y=-2 x+1$correct
  3. C.$y=2 x-3$
  4. D.$y=2 x+1$

Answer

B. $y=-2 x+1$

Explanation

【详解】 $\because f(x)=x^{4}-2 x^{3}, \therefore f^{\prime}(x)=4 x^{3}-6 x^{2}, \therefore f(1)=-1, f^{\prime}(1)=-2$, 因此, 所求切线的方程为 $y+1=-2(x-1)$, 即 $y=-2 x+1$. 故选: B.

Practice more Gaokao questions

Answer thousands more real Gaokao previous-year questions free, get graded instantly, and climb the global ranked leaderboard.

Practice Gaokao free →

More Gaokao Math questions