Flash Flash Revolution - View Single Post - [Highschool - Calculus] Finding Equation of a Tangent Line and Normal Line

**dag12** · 10-22-2008, 08:27 PM

3) Use the definition f'(a) = the limit as x->a f(x)-f(a)/x-a to find the derivative of f(x) = 1/x at x=3.

so.
lim [x->a] [ f(x) - f(a) ] / (x - a)
lim [x->a] [ 1/x - 1/a ] / (x - a)
lim [x->a] [ (a - x) / ax ] / (x - a)
lim [x->a] [ - (x - a) / ax ] / (x - a)
lim [x->a] - 1 / ax
= - 1 / x^2

f'(x) = - 1 / x^2

So when x = 3,
f'(3) = - 1/9

10-22-2008, 08:27 PM	#6
dag12 FFR Simfile Author Join Date: Dec 2004 Posts: 468	Re: [Highschool - Calculus] Finding Equation of a Tangent Line and Normal Line 3) Use the definition f'(a) = the limit as x->a f(x)-f(a)/x-a to find the derivative of f(x) = 1/x at x=3. so. lim [x->a] [ f(x) - f(a) ] / (x - a) lim [x->a] [ 1/x - 1/a ] / (x - a) lim [x->a] [ (a - x) / ax ] / (x - a) lim [x->a] [ - (x - a) / ax ] / (x - a) lim [x->a] - 1 / ax = - 1 / x^2 f'(x) = - 1 / x^2 So when x = 3, f'(3) = - 1/9