the slope of the tangent line at x is f'(x) = cosx
so at x = π/3 the slope is 1/2
Now you have a point and a slope, so
y-√3/2 = 1/2 (x - π/3)
You can see from the graphs at
https://www.wolframalpha.com/input/?i=plot+y%3Dsinx%2C+y+%3D+1%2F2+%28x+-+%CF%80%2F3%29+%2B+%E2%88%9A3%2F2
that the line is very close to the curve for a small interval near x=π/3
find the linerization L(x) of the function a. f(x)=sin(x), a=pi,3
1 answer
1 answer