Finding the Equation of a Tangent Line Using Basic Calculus
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Find an equation of the line tangent to the graph of the curve y = 2^x + ln x at x = 1
(^ means exponent)
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Solution Summary
This solution shows how to find the equation of the tangent line to y = 2^x + ln x, at x = 1, using some basic calculus. The steps involved and the knowledge required to solve the problem are provided.
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In order to find a tangent line to a curve, we need to things:
1. A point on the curve
2. The slope of the curve at that point
The point is given by the x-value in the problem: x = 1. We just need to plug that into the equation y = 2^x + ln x:
At x = 1, y = 2^1 + ln 1 = 2 + 0 = 2. Remember that any number to the first power is that number, and that the logarithm of 1 is 0 (e, or any number, to the 0th power, is 1). So the point (x,y) = (1,2) is on the curve.
Up to this point is basic algebra. The slope is where the calculus comes in. ...
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