Calc2.42

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Find the equation of the tangent line to the graph f(x)=xe^{x}+x+5 when x=0.

To find the equation of a line, we need two points or a point and the slope. Since the derivative gives the slope of the tangent line, find f'(0)\,. We already know a point on the tangent line as it must be on the graph at x=0.

f'(x)=e^{x}+xe^{x}+1\,

and

f'(0)=e^{0}+0+1=2\,

So the slope of the tangent line to f(x) at the point (0,5) is 2. Now, to find the equation of the tangent line, we can use the point and slope by using the point-slope form.

y-0=2(x-5)\,


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