betzabeth8 betzabeth8

02-03-2017
Mathematics

contestada

Find an equation of the tangent line to the curve at the given point.
y = 4e^x + x, (0, 4)

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LammettHash LammettHash

02-03-2017

[tex]y=4e^x+x\implies y'=4e^x+1[/tex]

At the point (0,1), the derivative has the value of [tex]y'=4e^0+1=5[/tex], so this is the slope of the tangent line. The equation for the line is then

[tex]y-4=5(x-0)\implies y=5x+4[/tex]

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