# Calculus - Derivative

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?

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Hurkyl
Staff Emeritus
Gold Member
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.

ahh, tricky tricky :) Thanks hurkyl

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 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

[;)]

That just takes too long

HallsofIvy