Nano-Passion
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Case closed![/color]
I'm reviewing for a test and I'm surprised of this. I've did countless problems harder than this.. for some reason every time I use the constant rule I get it wrong.. I want to understand.. WHY?!?
Determine the points at which the graph of the function has a horizontal line.
g(x)=\frac{8(x-2)}{e^x}
g(x)=\frac{8(x-2)}{e^x}
By the constant rule:
=8 (\frac{x-2}{e^x}
Definition of quotient rule with constant
c \frac{\frac{d}{dx} f(x) g(x) - \frac{d}{dx} g(x) f(x)}{[g(x)]^2}
8 \frac{1(e^x)-e^x(x-2)}{e^{2x}}
Distribute e^x
=8 \frac{e^x - xe^x - 2e^x}{e^{2x}}
Divide by e^x
= 8 \frac{-x-2}{e^x}
= \frac{-8x-16}{e^x}
Horizontal line (0 slope) is at g'(-2)
g(2)= \frac{-8(x-2}{e^x}
g(2) = \frac{-32}{e^-2}
g(2) = -32e^2
So g(x) has a horizontal tangent at (-2,-32e^2)
But the right answer is supposed to be horizontal line slope at g'(3) and horizontal tangent at (3,\frac{8}{e^3})
What am I doing wrong? Am I using the constant rule the wrong way? It makes me go crazy because I know I have all the basic derivative rules in check. Please help!
Homework Statement
I'm reviewing for a test and I'm surprised of this. I've did countless problems harder than this.. for some reason every time I use the constant rule I get it wrong.. I want to understand.. WHY?!?
Determine the points at which the graph of the function has a horizontal line.
g(x)=\frac{8(x-2)}{e^x}
The Attempt at a Solution
g(x)=\frac{8(x-2)}{e^x}
By the constant rule:
=8 (\frac{x-2}{e^x}
Definition of quotient rule with constant
c \frac{\frac{d}{dx} f(x) g(x) - \frac{d}{dx} g(x) f(x)}{[g(x)]^2}
8 \frac{1(e^x)-e^x(x-2)}{e^{2x}}
Distribute e^x
=8 \frac{e^x - xe^x - 2e^x}{e^{2x}}
Divide by e^x
= 8 \frac{-x-2}{e^x}
= \frac{-8x-16}{e^x}
Horizontal line (0 slope) is at g'(-2)
g(2)= \frac{-8(x-2}{e^x}
g(2) = \frac{-32}{e^-2}
g(2) = -32e^2
So g(x) has a horizontal tangent at (-2,-32e^2)
But the right answer is supposed to be horizontal line slope at g'(3) and horizontal tangent at (3,\frac{8}{e^3})
What am I doing wrong? Am I using the constant rule the wrong way? It makes me go crazy because I know I have all the basic derivative rules in check. Please help!
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