Find the relative extrema and the points of inflection (if any exist) of the function. Use a graphing utility to graph the function and confirm your results.

Question

f(x)=(5ex-5e-x)/2

Answer 1

f(x) = (5e^x - 5e^-x) / 2

f'(x) = (5e^x + 5e^-x) / 2 > 0 for all x.

So, f(x) is increasing on (-∞, ∞)

Therefore, there are no relative extrema.

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f"(x) = (5e^x - 5e^-x) / 2

f"(x) = 0 when 5e^x = 5e^-x

e^2x = 1

2x = 0

So, x = 0

When x < 0, f"(x) < 0. So, f(x) is concave down.

When x > 0, f"(x) > 0, So, f(x) is concave up

Inflection point: (0, f(0)) = (0, 0)

Answer 2

3rd quad

-6.5,-001.68

-5.75,-.0765

-4.7,-.0219

-2.9,-.977

0,0

Repeat opposite on 1st quad