1) Let f(x) be a continuous, everywhere differentiable functionand g(x) be its derivative. If f(c) = n and g(c) = d, write theequation of the tangent line at x = c using only the variables y,x, c, n, and d. You may use point-slope or slope-intercept but donot introduce more variables.
2) Let f(x) be a continuous, everywhere differentiable function.What kind information does f'(x) provide regarding f(x)?
3) Let f(x) be a continuous, everywhere differentiable function.What kind information does f''(x) provide regarding f(x)?
4) Let f(x) be a continuous, everywhere differentiable function.What kind information does f''(x) provide regarding f'(x)?
5) Let h(x) be a continuous function such that h(a) = m andh'(a) = 0. Is there enough evidence to conclude the point (a, m)must be a maximum or a minimum? Explain.
