How do you find the tangent line of f(x)=3x\sin x^{2}

omdw1u

omdw1u

Answered question

2022-02-18

How do you find the tangent line of f(x)=3xsinx2 at x=-1?

Answer & Explanation

asserena3wx

asserena3wx

Beginner2022-02-19Added 7 answers

f(x)=3xsin(x2)
Use the product rule to find f'(x).
f(x)=sin(x2)ddx[3x]+3xddx[sin(x2)]
3sin(x2)+6x2cos(x2)
f(1)=3sin(1)2.524
Thus, the tangent line passes through the point (-1, -2.524).
f(1)=3sin(1)+6cos(1)5.766
The slope of the tangent line is 5.766.
Write this in point-slope form:
y+2.254=5.766(x+1)

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