What is the equation of the tangent line

Juliet Jackson

Juliet Jackson

Answered question

2022-03-14

What is the equation of the tangent line of f(x)=x2+2x at x=3?

Answer & Explanation

danomangli

danomangli

Beginner2022-03-15Added 3 answers

Differentiate the equation to find the gradient.
f'(x)=2x+2
At the point x=3 this equals 8 which is the gradient.
The equation for the tangent is y=mx+c where m is the gradient and c is the y-intercept.
We can find c by using the coordinates of the specified point.
At x=3, y=32+2+23=15
This point is also on the tangent line, so we can say 15=8*3+c
Therefore c=15-24=-9
The tangent line is y=8x-9

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