Question:
The maximum slope of the curve $y=\frac{1}{2} x^{4}-5 x^{3}+18 x^{2}-19 x$ occurs at the point:
Correct Option: , 2
Solution:
$\frac{d y}{d x}=2 x^{3}-15 x^{2}+36 x-19$
Let $f(x)=2 x^{3}-15 x^{2}+36 x-19$
$f^{\prime}(x)=6 x^{2}-30 x+36=0$
$x^{2}-5 x+6=0$
$x=2,3$
$f "(x)=12 x-30$
$f "(x)<0$ for $x=2$
At $x=2$
$y=8-40+72-38$
$y=72-70=2$
$\Rightarrow(2,2)$
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