SOLUTION: 1. f(x)= x^3 - 3x^2 + x + 1 2. f(x)=sinx + 1 on [-2pi, 2pi] 3. f(x)=(x^2)(e^(-4x)) (a) Find the x- and y-intercepts of the function. (b) Draw a number line for f: (c) Find a

Question 428180: 1. f(x)= x^3 - 3x^2 + x + 1
2. f(x)=sinx + 1 on [-2pi, 2pi]
3. f(x)=(x^2)(e^(-4x))
(a) Find the x- and y-intercepts of the function.
(b) Draw a number line for f:
(c) Find all critical numbers for f prime:
(d) Draw a number line for f prime:
(e) Find all zeros of f double prime:
(f) Draw a number line for f double prime:
(h) Find all inflection points of f:
(i) Sketch the graph of f. Label all inflection points. Label your axes.
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
I'll get you started:

If f(x) = , then f'(x) = and f''(x) = (simply applying the power rule).
If f(x) = then f'(x) = and f''(x) = .
#3 is a little harder to differentiate because we need to apply the product rule twice. If f(x) = then f'(x) = . Differentiating again, f''(x) = . I'll let you handle the 24 parts of the problem.
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