- #1
DMOC
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Homework Statement
Let h be a function defined for all x =/= such that h(4) = -3 and the derivative of h is given by h ' (x) = (x[tex]^{2}[/tex]-2)/x for all x=/=0.
a) Find all values of x for which the graph of h has a horizontal tangent, and determine whether h has a local maximum, a local minimum, or neither at each of these values. Justify your answers.
b) On what intervals, if any, is the graph of h concave up? Justify your answer.
c) Write an equation for the line tangent to the graph of h at x = 4.
d) Does the line tangent to the graph of h at x = 4 lie abov eor below the graph of h for x>4? Why?
Homework Equations
I don't think there are any.
The Attempt at a Solution
Let's try part a, and I'll do the other three once I get part a down.
So for part a, I need to find the values of x for which the graph of h has a horizontal tangent. Unfortunately, I'm not sure how to accomplish this, and I know I can't use a calculator.
So I'm thinking that the correct way to do this problem is to find the original graph of h(x). I have h'(x). However, I'm not sure how to actually find the original equation. When I do some fiddling around with h'(x), I get this:
h'(x) = x - 2x[tex]^{-1}[/tex]
And I'm not sure how to find the original equation, or even if that's the correct way to do this problem.