Calculus - Derivative

1. Sep 28, 2003

Chris_w

find the value of the derivative of f(x)=-2(x-3)^2 at the point (2,-2)

I am a little confused as to why they give you a point... how can I solve this?

2. Sep 28, 2003

Hurkyl

Staff Emeritus
Basically, they just gave you an extra, useless bit of information. (Though that extra bit of information will be essential in problems in later sections)

They just want f'(2) and are telling you that f(2) = -2.

3. Sep 28, 2003

Chris_w

ahh, tricky tricky :) Thanks hurkyl

4. Sep 29, 2003

FrostScYthe

f(x)=-2(x-3)^2
f'(x) = -4(x-3)

f'(2) = -4(2-3)
f'(2) = 4

4 is the derivative of f(x) at point x=2 which is also THE SLOPE
and if you have a point (2,-2) and a SLOPE gives you an equation, which is the equation of the tangent line at that point. Tangent is same thing as Derivative except that in the derivative they are too lazy to write an equation for that line, they only put the slope

I hope that helps, don't hate me too much if i'm confusing you

5. Oct 5, 2003

hawaiidude

or you can use teh "good" old lim h~~>0 f(x+deltax)-f(x)/ delta x...in your case f(x)=-2(x-3)^3 ....or you can use the power rule for all functions cx^2=2cx

6. Oct 23, 2003

FrostScYthe

[;)]

That just takes too long

7. Oct 23, 2003

HallsofIvy

Please don't write nonsense: cx^2 is NOT equal to 2 cx. Yes, I know what you MEANT but that was what you wrote. Also the power rule does not apply to "all functions".

8. Oct 23, 2003

hawaiidude

ok mr smart ass