What is the equation of the tangent line

Jayleen Aguirre

Jayleen Aguirre

Answered question

2022-04-10

What is the equation of the tangent line of f(x)=2x2+5x+2 at x=-1

Answer & Explanation

Colin Collins

Colin Collins

Beginner2022-04-11Added 10 answers

To find a line, we must know its slope and one of its points.
The slope is given by the derivative evaluated at the requested point, so we have
f(x)=4x+5f(1)=4+5=9
The point is of course the point on the graph (-1, f(-1)), which is (-1, -5)
Once the slope and a point are known, the equation of the line is given by
yy0=m(xx0)
y+5=9(x+1)
y=9x+9-5=9x+4

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