38.
\(f\left(x\right)=a_0+a_1x+a_2x^2+...+a_{60}x^{60}\)
\(\Rightarrow f'\left(x\right)=a_1+2a_2x+3a_3x^2+...+60a_{60}x^{59}\)
\(\Rightarrow f''\left(x\right)=2a_2+6a_3x+...+3540a_{60}x^{58}\)
Thay \(x=1\)
\(\Rightarrow f''\left(1\right)=2a_2+6a_3+12a_4+...+3540a_{60}\)
\(\Rightarrow T=2024a_0+f''\left(1\right)\)
\(a_0=f\left(0\right)=1\)
\(f'\left(x\right)=30\left(1-3x+2x^2\right)^{29}.\left(4x-3\right)\)
\(f''\left(x\right)=120\left(1-3x+2x^2\right)^{29}+30.29.\left(1-3x+2x^2\right).\left(4x-3\right)^2\)
\(\Rightarrow f''\left(1\right)=120.0+30.29.0.1=0\)
\(\Rightarrow T=2024.1+0=2024\)
41.
\(x^2.f'\left(x\right)-x.f\left(x\right)=-x^3.e^{x^2}+x.\left[f'\left(x\right)-f\left(x\right)\right]\)
\(\Leftrightarrow\left(x^2-x\right).f'\left(x\right)=-x^3.e^{x^2}\)
\(\Rightarrow f'\left(x\right)=\dfrac{-x^2.e^{x^2}}{x-1}\)
\(\Rightarrow f''\left(x\right)=\dfrac{-x^2+2x}{\left(x-1\right)^2}.e^{x^2}-\dfrac{2x^3}{x-1}.e^{x^2}\)
\(\Rightarrow f''\left(3\right)=-\dfrac{3}{4}.e^9-27e^9=\dfrac{-111}{4}e^9\)
\(\Rightarrow P=\dfrac{3.111.4}{9}=148\)
42.
\(y'=-\dfrac{1}{3}x^3+2x^2+5x\)
\(y''=-x^2+4x+5\)
\(-x^2+4x+5>0\Rightarrow-1< x< 5\)
Đáp án có gì đó sai sai (mặc dù chọn A chắc cũng được)
43.
\(f'\left(x\right)=-2sin\left(2x-\dfrac{\pi}{3}\right)\)
\(f''\left(x\right)=-4cos\left(2x-\dfrac{\pi}{3}\right)\)
\(f''\left(x\right)=4\Leftrightarrow cos\left(2x-\dfrac{\pi}{3}\right)=-1\)
\(\Leftrightarrow2x-\dfrac{\pi}{3}=\pi+k2\pi\)
\(\Leftrightarrow x=\dfrac{2\pi}{3}+k\pi\)
\(\Rightarrow x=\dfrac{2\pi}{3}\)
cho đáp án và giải thích giùm mình với ạ
