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Find an equation of the tangent line to the graph of the function at the given point.

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Find an equation of the tangent line to the graph of the function at the given point.

asked Jan 31, 2015 in CALCULUS by anonymous

1 Answer

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Step 1:

The function is and point is .

Change-of-base formula for logarithms : .

Apply derivative on each side with respect to .

.

Step 2:

Find slope at the point .

Substitute in derivative of the function.

image.

Slope of a tangent line is image.

Point - slope form of a line equation is .

Substitute and image in point - slope form.

image

The tangent line equation is image.

Step 3:

Graph :

Graph the function and tangent line is image :

image

Solution :

The tangent line equation is image.

answered Jan 31, 2015 by joseph Apprentice

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