<s>[INST] Find the largest positive value of $x$ at which the curve $y = (2x + 7)^6 (x - 2)^5$ has a horizontal tangent line. I need help with the following question.
Find the largest positive value of x at which the curve:
$$y = (2x + 7)^6 (x - 2)^5$$ 
has a horizontal tangent line.
 [/INST] Hint: $\displaystyle{\frac{dy}{dx} = \left(12(2x+7)^5(x-2)^5+5(2x+7)^6(x-2)^4 \right) = 0}$ , in other words
$\displaystyle{\frac{dy}{dx} = (2x+7)^5(x-2)^4(22x+11) = 0}$ at what points?

$\displaystyle{\frac{dy}{dx} = 0}$ at $x=-\frac{7}{2}, x=2, x=-\frac{1}{2}$

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