![image](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E3-2x%5E2%2B3%0A%5C%5C%5C%0Af%60%28x%29%3D3x%5E2-4x%0A%5C%5C%5C%0Af%60%28a%29%3Df%60%28-1%29%3D3%2B4%3D7%0A%5C%5C%5C%0Ak%3D7%3E0+%5CRightarrow++%5Calpha+%3C90)
0 \Rightarrow \alpha <90" alt="f(x)=x^3-2x^2+3
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f`(x)=3x^2-4x
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f`(a)=f`(-1)=3+4=7
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k=7>0 \Rightarrow \alpha <90" align="absmiddle" class="latex-formula">
![image](https://tex.z-dn.net/?f=f%28x%29%3D+%5Cfrac%7Bx-1%7D%7Bx%2B3%7D+%0A%5C%5C%5C%0Af%60%28x%29%3D+%5Cfrac%7B%28x-1%29%60%28x%2B3%29-%28x-1%29%28x%2B3%29%60%7D%7B%28x%2B3%29%5E2%7D+%3D%5Cfrac%7Bx%2B3-x%2B1%7D%7B%28x%2B3%29%5E2%7D%3D%5Cfrac%7B4%7D%7B%28x%2B3%29%5E2%7D%0A%5C%5C%5C%0Af%60%28a%29%3Df%60%281%29%3D%5Cfrac%7B4%7D%7B%281%2B3%29%5E2%7D%3D0.25%0A%5C%5C%5C%0Ak%3D0.25%3E0+%5CRightarrow++%5Calpha+%3C90)
0 \Rightarrow \alpha <90" alt="f(x)= \frac{x-1}{x+3}
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f`(x)= \frac{(x-1)`(x+3)-(x-1)(x+3)`}{(x+3)^2} =\frac{x+3-x+1}{(x+3)^2}=\frac{4}{(x+3)^2}
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f`(a)=f`(1)=\frac{4}{(1+3)^2}=0.25
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k=0.25>0 \Rightarrow \alpha <90" align="absmiddle" class="latex-formula">