Question

Find the equation of the line tangent to f(x)=2x^2+2x=1 at (1,2). Walk me through please!

Answer 1

we have to find tangent at (1,2) on the curve of f(x)
to find the equation of the tangent , we need its slope
slope is given by f'(x) at the point 1,2
or f'(1)
f'(x)=4x+2
slope is value of f'(x) at the point (1,2)
f'(1)=6
Tangent's slope is 6 and it passes through 1,2
we know equation of a line passing through a point x1, y1 and having slope m
is given by
(y-y1)/(x-x1)=m
(y-2)/(x-1)=6
y-2=6x-6
or y=6x-4
this is the tangent's equation