QuestionLet be a.function defined for all , such that , and the derivative of is given by for all . A. Find all values of for which the graph of has a horizontal tangent, and determine whether has a local maximum a local minimum, or neither at each of these values. Justify your answers. B. On what intervals, if any, is the graph of concave up? Justify your answer. C. Write an equation for the line tangent to the graph of at . D. Does the line tangent to the graph of at lie above or below the graph of for ? Why?
Studdy Solution
A. Horizontal tangents at (local max) and (local min).
B. Concave up on and .
C. Tangent line equation: .
D. The tangent line lies below the graph for due to the concavity of .
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