How do you find the equation of the line tangent to the graph of y=x^2 at x=2?

1 Answer
Jul 27, 2015

I found: y=4x-4

Explanation:

First you need the slope m of the tangent. You find it evaluating the derivative of your function in x=2:
y'=2x
so m=y'(2)=2*2=4 this is the slope of the tangent at the point of coordinates:
x_0=2 and y_0=x^2=2^2=4;
now you can use the relationship:
y-y_0=m(x-x_0)
y-4=4(x-2) rearranging:
y=4x-8+4
y=4x-4

Graphically:
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