# Derivates for equation of tangent and normal

• Oct 24th 2007, 05:09 PM
Truthbetold
Derivates for equation of tangent and normal
If f(2)= 3 and f'(2)= 5, find an equation (a) the tangent line, and (b) the normal line to the graph of y=f(x) at the point where x=2.

Guess:
f(2)=3 refers to the answer of a basic derivative ( lim as h--> 0 $\frac {f(x-h) -f(x)}{h}$ )of an unknown equation with x=2.

f'(2)=5 refers to the answer of the same equation in the other definition
lim as x--> a $\frac {f(x)-f(a)}{x-a}$ with x=2.

Either that f(2) in some equation of the derivative = 3 and 5.
I'm inclined to believe the latter.

Thanks!
• Oct 24th 2007, 05:21 PM
Jhevon
Quote:

Originally Posted by Truthbetold
If f(2)= 3 and f'(2)= 5, find an equation (a) the tangent line, and (b) the normal line to the graph of y=f(x) at the point where x=2.

Guess:
f(2)=3 refers to the answer of a basic derivative ( lim as h--> 0 $\frac {f(x-h) -f(x)}{h}$ )of an unknown equation with x=2.

f'(2)=5 refers to the answer of the same equation in the other definition
lim as x--> a $\frac {f(x)-f(a)}{x-a}$ with x=2.

Either that f(2) in some equation of the derivative = 3 and 5.
I'm inclined to believe the latter.

Thanks!

you're thinking too hard. f(2) = 3 means the line passes through (2,3), f'(2) = 5 means the slope of the line is 5 at the point x = 2. just use the point slope form, no calculus needed (the normal line of course has slope -1/5, passing through the same point, again, use the point slope form for this)
• Oct 24th 2007, 05:49 PM
Truthbetold
Oooooooooooooooooooooooooooooooooooooooooooh!
Got it.

Is there a difference in meaning for f(x) and f'(x)?
My book gives the impression that they all mean, when it comes down to the nitty gritty, the same function.
• Oct 24th 2007, 05:52 PM
Jhevon
Quote:

Originally Posted by Truthbetold
Oooooooooooooooooooooooooooooooooooooooooooh!
Got it.

Is there a difference in meaning for f(x) and f'(x)?
My book gives the impression that they all mean, when it comes down to the nitty gritty, the same function.

no. f(x) is a function, f'(x) is the derivative of the function f(x), the ' means first derivative. if you had f''(x) it would mean the second derivative of f(x), which means you take the derivative twice and so on