What is the slope of \(\displaystyle{f{{\left({x}\right)}}}=-{x}{e}^{{{x}}}+{2}{x}\) at

fellesturduj

fellesturduj

Answered question

2022-03-15

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

Answer & Explanation

Spakatjlb

Spakatjlb

Beginner2022-03-16Added 4 answers

f(x)=xex+2x
f(x)=xex+(1)ex+2 Product rule and power rule
=ex(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:
duramadregtw

duramadregtw

Beginner2022-03-17Added 2 answers

Given -
y=xex+2x
Its slope is defined by its first derivative.
dydx=[xex(1)+ex(1)]+2
dydx=xexex+2
Its slope at x=1
dydx=(1)e1e1+2
dydx=e1e1+2=3.4365

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