I have this assignment due wednesday.. and I've started it.. but I want to make sure I'm on the right track.. and some of them I have no clue where to start. Anyways.. if anyone can help it would be much appreciated
1. Determine the derivative of
f(x)= 2x^2 - 1
from first principles. Use the quotient rule to verify your answer.
2. The graph of
f(x)= ax + b
has a horizontal tangent line at (2,-1). Determine the values of a and b.
3. The tangent line to the curve defined by
g(x)= x^4 - 2x^3 +3
at x= -1 intersects the curve at two other points P and Q. Determine the coordinates of P and Q algebraically. Illustrate this situation with a graph. (to graph g you need to create a table of values)
HINT: You need to research L'hopital's rule in order to complete this question
I have no clue what L'hopital's rule is, because we've never learned it, so if someone could also explain that to me.. that would be great.
I'll show you a way where you don't have to use rule de l'Hopital. (There is actually no need to use this rule!)
Then g(-1) = 1
The tangent t becomes:
Calculating the intercept mean: g(x) = t(x):
Multiply by (-6x):
. You already know that x = -1 must be a solution of this equation. So divide the LHS of the equation by (x+1) and you'll get:
So you get the additional solutions: x = 1 and x = 3.
I'll leave the rest for you. Good luck!