Find an equation of the line tangent to the graph of $y=\frac{e^{-9 x}}{x^{9}+1}$ at the point where x = 0.
A) $y=-9 x+1$
B) $y=9 x$
C) $y=9 x+1$
D) $y=-9 x$

Name: Find an equation of the line tangent to the graph of $y=\frac{e^{-9 x}}{x^{9}+1}$ at the point where x = 0. A) $y=-9 x+1$ B) $y=9 x$ C) $y=9 x+1$ D) $y=-9 x$
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Question

Quizplus · Accepted Answer

The function value at x=0 is $y(0)=\frac{e^{0}}{0^{9}+1}=1$. The derivative at x=0 is found using the quotient rule, resulting in a slope of -9. Thus, the tangent line is $y=-9x+1$.

Find an Equation of the Line Tangent to the Graph y=e−9xx9+1y=\frac{e^{-9 x}}{x^{9}+1}y=x9+1e−9x​

Find an Equation of the Line Tangent to the Graph $y=\frac{e^{-9 x}}{x^{9}+1}$