# finding an equation of the tangent line to a curve at the given point in MATLAB

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Kyle Johnson on 27 Jan 2021
Answered: Birdman on 27 Jan 2021
I tried looking for and solving this for an hour and I am stumped.
the question I am trying to have answered is: find an equation of the tangent line to the curve at the given point y=4x-3x^2, (2,-4)

Birdman on 27 Jan 2021
Actually, it is quite simple to do. For instance, let's define the equation symbolically in MATLAB:
syms y(x)
y(x)=4*x-3*x^2;
Then, take the derivative:
dy(x)=diff(y,x)
which would be
4-6*x
At this point, you can find the slope of the tangent line at point (2,-4) by inserting 2 into the above equation, which would be
4-6*(2)=-8
You know that the slope of tangent line is -8, but you should also find the value of y for that tangent line. Consider it as
y=-8*x+c
Then find the c by simply
-4=-8*(2)+c
where c would be 12.
If you plot both curves in the same figure, you will get where the blue line is the original equation and red line is tangent line.