Derivatives: if f(x) = 7 + 7x - 5x^2, find f'(-1)

[rjcj]

Learning derivatives and having trouble with this problem: if f(x)=7+7x-5x^2, find f'(-1). I thought it was simple substitution of -1 for x, but that's not it. Please help.

 

[royhaas]

Re: Derivatives

Take the derivative first, then substitute the numerical value.

 

[sgtpepper]

First you should know that...

f(x) means a function of x
f'(x), also called "f-prime of x" is the derivative of the function of x.
f''(x), called "f-double-prime of x" is the second derivative of the function of x.
f'''(x), called "f-triple-prime of x" is the third derivative of the function of x.
etc.
So, f'(-1) means evaluate the derivative of f(x) when x equals -1. That means you have to first take the derivative of f(x):

f(x) = 7 + 7x - 5x^2
f'(x) = 0 + 7 - 10x

Now evaluate the derivative for when x = -1. In other words, plug in -1 for x in the derivative:

f'(x) = 0 + 7 - 10x
f'(-1) = 7 - 10(-1)
f'(-1) = 7 - (-10)
f'(-1) = 7 + 10
f'(-1) = 17


Hope that helps you and that I didn't make any mistakes!