Thread: tangent line

Assume that f(x) is differentiable at x=a.state the equation of tangent line to the graph of f(x) at point (a,f(a))

Originally Posted by bobby77

Assume that f(x) is differentiable at x=a.state the equation of tangent line to the graph of f(x) at point (a,f(a))

The equation of a line is
y = mx + b

We know the slope of the function at (a, f(a)): it is simply f'(a). Thus

f(a) = f'(a)*a + b

b = f(a) - f'(a)*a

So
y = f'(a)x + [f(a) - f'(a)*a]

-Dan

You can also use the formula,
If m is slope and (x_0,y_0) is point then equation is,
y-y_0=m(x-x_0)

Thus,
m=f'(a)
x_0=a
y_0=f(a)

Thus,
y=f'(a)x-f'(a)a+f(a)