How do you find the points where the graph of the function #y=x^6 * e^x# has horizontal tangents and what is the equation?
1 Answer
Oct 3, 2017
The equation of the tangent is
Explanation:
Given -
#y=x^6e^x#
Find the slope.
#dy/dx=x^6e^x+e^x.6x^5=x^6e^x+6x^5e^x #
The tangent must draw to a point on the curve where its slope is zero. We have to find the coordinates of that point.
Set first derivative equal to zero.
#x^6e^x+6x^5e^x=0#
Solve it for
#x(x^5e^x+6x^4e^x)=0#
#x=0/(x^5e^x+6x^4e^x)=0#
At
The equation of the tangent is