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Let f(x) be a continuous, everywhere differentiable function. What kind information does f'(x) provide regarding f(x)?...

Let f(x) be a continuous, everywhere differentiable function. What kind information does f'(x) provide regarding f(x)?

Let f(x) be a continuous, everywhere differentiable function. What kind information does f''(x) provide regarding f(x)?

Let f(x) be a continuous, everywhere differentiable function. What kind information does f''(x) provide regarding f'(x)?

Let h(x) be a continuous function such that h(a) = m and h'(a) = 0. Is there enough evidence to conclude the point (a, m) must be a maximum or a minimum? Explain.

Write a function k(x) such that k(5) = -3, k'(5) = 0, and k''(5) < 0. Algebraically show your function k(x) does possess these attributes.

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