How to find the equation of the line tangent to the graph of f at the indicated value of x? f(x)= 4 - lnx ; x=1
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To find the equation of the line tangent to the graph of f at x=1, we need to find the derivative of f(x) and evaluate it at x=1.
The derivative of f(x) can be found using the power rule and the chain rule. The derivative of 4 is 0, and the derivative of ln(x) is 1/x. Therefore, the derivative of f(x) is 0 - 1/x.
Evaluating the derivative at x=1, we have 0 - 1/1 = -1.
So, the slope of the tangent line at x=1 is -1.
To find the equation of the line, we need a point on the line. Since the line is tangent to the graph of f at x=1, we can use the point (1, f(1)).
Plugging x=1 into f(x), we have f(1) = 4 - ln(1) = 4 - 0 = 4.
Therefore, the point on the line is (1, 4).
Using the point-slope form of a line, y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line, we can substitute the values:
y - 4 = -1(x - 1)
Simplifying, we have y - 4 = -x + 1.
Rearranging the equation, we get y = -x + 5.
So, the equation of the line tangent to the graph of f at x=1 is y = -x + 5.
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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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