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riadik2000 [5.3K]
3 years ago
12

Math assignment cant get it

Mathematics
1 answer:
kupik [55]3 years ago
8 0

Answer:

y = -1/2x + (-1)

Step-by-step explanation:

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3 years ago
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Over [174]
\bf f(x)=(x-6)e^{-3x}\\\\&#10;-----------------------------\\\\&#10;\cfrac{dy}{dx}=1\cdot e^{-3x}+(x-6)-3e^{-3x}\implies \cfrac{dy}{dx}=e^{-3x}[1-3(x-6)]&#10;\\\\\\&#10;\cfrac{dy}{dx}=e^{-3x}(19-3x)\implies \cfrac{dy}{dx}=\cfrac{19-3x}{e^{3x}}

set the derivative to 0, solve for "x" to get any critical points
keep in mind, setting the denominator to 0, also gives us critical points, however, in this case, the denominator will never be 0, so... no critical points from there

there's only 1 critical point anyway, and do a first-derivative test on it, check a number before it and after it, to see what sign the derivative has, and thus, whether the graph is going up or down, to check for any extrema
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