What is the equation of the tangent line of $f (x) = sin π x$ $f(x)=sinpix$ at $x = 3$ $x=3$ ?

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Answer 1 · 2015-12-30T05:31:39

$y = π (3 - x)$ $y = pi(3-x)$

$Graph of f (x)$ $color(blue)("Graph of "f(x))$
graph{sin(pix) [-10, 10, -5, 5]}

To construct a straight line, one needs either two points, or a point and the gradient. In this case, the latter would be more appropriate.

$f (3) = 0$ $f(3) = 0$

We know that the line passes through the point $(3, 0)$ $(3,0)$ .

$f'(x) = picospix$

$f'(3) = -pi$

We know that the gradient of the line is $-pi$ .

$-pi = frac{y-0}{x-3}$

Equation of tangent line:

$y = pi(3-x)$

$color(blue)("Graph of tangent line")$
graph{pi(3-x) [-10, 10, -5, 5]}

What is the equation of the tangent line of f(x)=sinpix f(x)=sinπx f(x)=sinpix at x=3 x=3 x=3 ?