How to find the value of a?

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Answer 1 · 2018-04-04T05:50:14

#a=1#

.

#y=2e^x#

We take the derivative and evaluate it at the given point:

#dy/dx=2e^x#

#slope=m=2e^a#

The equation of the tangent line is:

#y=mx+b#

#y=2xe^a+b#

We plug in the coordinates of the given point to solve for #b#:

#2e^a=2ae^a+b#

#b=2e^a-2ae^a#

Therefore, the equation of the tangent line at the given point is:

#y=2xe^a+2e^a-2ae^a#

Since the line passes through the origin #(0,0)#, we will use these coordinates to solve for #a#

#0=2(0)e^a+2e^a-2ae^a#

#2ae^a=2e^a#

#a=1#