How do you find the slope of the tangent line

Shayla Lyons

Shayla Lyons

Answered question

2022-02-10

How do you find the slope of the tangent line to the graph of the function f(x)=xex at x=7?

Answer & Explanation

mixtyggc

mixtyggc

Beginner2022-02-11Added 15 answers

Explanation:
We are given: f(x)=xex
To find the slope of the tangent line, we plug in f'(x) for x=7, i.e. f'(7).
So, we differentiate using the product rule, which states that,
ddx(f(x)g(x))=f(x)g(x)+f(x)g(x)
And so, we got:
f(x)=(x)ex+x(ex)
=1ex+xex
=xex+ex
=ex(x+1)
We plug in x=7, and get,
f(7)=e7(7+1)
=8e7

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