How do you graph the derivative of #f(x) = log (x)#?
See below.
The y axis is a vertical asymptote.
The x axis is a horizontal asymptote.
GRAPH:
graph{y=1/x [-16.02, 16.01, -8.01, 8.01]}
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To graph the derivative of ( f(x) = \log(x) ), follow these steps:
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Find the derivative of ( f(x) ) using the differentiation rules. The derivative of ( \log(x) ) is ( \frac{1}{x} ).
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Plot the graph of ( \frac{1}{x} ) on the same coordinate system where ( x ) is positive, negative, and zero.
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The graph of ( \frac{1}{x} ) will have a vertical asymptote at ( x = 0 ) since division by zero is undefined.
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The graph will approach positive infinity as ( x ) approaches 0 from the positive side and negative infinity as ( x ) approaches 0 from the negative side.
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The graph of ( \frac{1}{x} ) will be decreasing for ( x > 0 ) and ( x < 0 ) since ( \frac{1}{x} ) is negative in these intervals.
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There will be no critical points since ( \frac{1}{x} ) has no points where its derivative is zero.
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Plot the graph according to these characteristics, and label the axes appropriately.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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- How do you use the first and second derivatives to sketch #f(x)= x^4 - 2x^2 +3#?
- What are the points of inflection, if any, of #f(x) =(x+4)/(x-2)^2#?

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