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Sketch the graph of each of the given functions by completing the following steps

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Question

please answer these questions as soon as possible, thank you

Sketch the graph of each of the given functions by completing the following steps: (show all the work for each step)

i) h(x)=x2 −25/9-x2

(a) Find the domain.

(b) Find any x and y intercepts.

(c) Is the function even or odd? Is it periodic?

(d) Find any/all vertical and horizontal asymptotes.

(e) Find the first derivative and list all intervals of increase and decrease.

(f) List any/all local max and min points.

(g) Find the second derivative and list all intervals where f is concave up and concave down. List any/all inflection points.

(h) Sketch the graph. Label all intercepts, asymptotes, local max and min points and points of inflection.

2. Show that the function f(x) = x4 − 4×3 + 4×2 − 24x − 1 has exactly tworeal roots. (Hint: use the Intermediate Value Theorem, Rolle’s Theorem,and that x3 − 3×2 + 2x − 6 = (x2 + 2)(x − 3).)

3. Show that the function g(x) = x4−6×2−8x+1 has exactly two real roots.(Hint: use the Intermediate Value Theorem, g0(x), and that x3−3x−2 =(x + 1)2(x − 2).)

 
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