SOLVED:Sketch a graph of a differentiable function y=f(x) that has the given properties. A local minimum value that is greater than one of its local maximum values.

SOLVED:The figure shows two parts of the graph of a continuous differentiable function f on [-10,4] . The derivative f^' is also continuous. To print an enlarged copy of the graph, go to MathGraphs.com. (a) Explain why f must have at least one zero in [-10,4] . (b) Explain why f^' must also have at least one zero in the interval [-10,4] . What are these zeros called? (c) Make a possible sketch of the function with one zero of f^' on the interval [-10,4] .

2. Sketch a graph of a differentiable function f such that r = 2 is the only critical number, f 0 on (2, ∞), lim(x→∞) f(x) = 6, and lim(x→-∞) f(x) = 6.