What is the slope of f(x)=-xe^x+2xf(x)=xex+2x at x=1x=1?

2 Answers
Sep 30, 2016

2(1-e) ~= -3.436562(1e)3.43656

Explanation:

f(x)= -xe^x+2xf(x)=xex+2x

f'(x)= -xe^x+(-1)e^x+2 Product rule and power rule

= -e^x(x+1)+2

The slope of f(x) at x=1 is given by f'(1)

f'(1) = -2e+2 = 2(1-e)

f'(1) ~= -3.43656

This can be seen by the graph of f(x) in the region of x=1 below:

graph{-xe^x+2x [-0.202, 2.498, -1.007, 0.343]}

Sep 30, 2016

Slope at x=1 is -3.4365

Explanation:

Given -

y=-xe^x+2x

Its slope is defined by its first derivative.

dy/dx=[-xe^x(1)+e^x(-1)]+2
dy/dx=-xe^x-e^x+2

Its slope at x=1

dy/dx=-(1)e^1-e^1+2
dy/dx=-e^1-e^1+2=-3.4365