# Thread: Derivates for equation of tangent and normal

1. ## 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$\displaystyle \frac {f(x-h) -f(x)}{h}$ )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 $\displaystyle \frac {f(x)-f(a)}{x-a}$ with x=2.

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

Thanks!

2. 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$\displaystyle \frac {f(x-h) -f(x)}{h}$ )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 $\displaystyle \frac {f(x)-f(a)}{x-a}$ 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)

3. 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.

4. 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