Exponential and Logarithmic Function Question

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Exponential and Logarithmic Function Question

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Onekeeper

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Exponential and Logarithmic Function Question

« on: May 12, 2018, 10:26:30 am »

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Hey, If possible could someone give me a hand at solving this question or ways of approaching these. Thanks in advance

Find the equation of the normal to the curve y=e^x at the point where x=3, in exact form.

The answer is x+e³y-3-e⁶=0

Thanks again

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RuiAce

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Re: Exponential and Logarithmic Function Question

« Reply #1 on: May 12, 2018, 10:29:16 am »

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$\text{The method is the same for every such question.}$
$y = e^x \implies \frac{dy}{dx}.\\ \text{At }x=3, y = e^3\text{ and }\frac{dy}{dx} = e^3.$
$\text{Because }\frac{dy}{dx}\text{ gives the gradient of the tangent,}\\ \text{the gradient of the normal is }-\frac1{e^3}.$
$\text{Hence using the point-gradient form}\\ \begin{align*}y - e^3 &= -\frac{1}{e^3}(x-3)\\ e^3y - e^6 &= 3 - x\\ x + e^3y - 3 - e^6 &=0\end{align*}$

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Onekeeper

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Re: Exponential and Logarithmic Function Question

« Reply #2 on: May 12, 2018, 10:31:08 am »

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Awesome, Thanks very much!

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