Identifying Extrema
In Exercises 15–18:
a. Find the open intervals on which the function is increasing and those on which it is decreasing.
b. Identify the function’s local and absolute extreme values, if any, saying where they occur.
Finding Indefinite Integrals
In Exercises 17–56, find the most general antiderivative or indefinite integral. You may need to try a solution and then adjust your guess. Check your answers by differentiation.
∫(−2cost) dt
Finding Extrema from Graphs
In Exercises 11–14, match the table with a graph.
41. Among all triangles in the first quadrant formed by the x-axis, the y-axis, and tangent lines to the graph of y=3x-x^2, what is the smallest possible area?
Initial Value Problems
Solve the initial value problems in Exercises 71–90.
dy/dx = 3x⁻²ᐟ³, y(−1) = −5
Identify the inflection points and local maxima and minima of the functions graphed in Exercises 1–8. Identify the open intervals on which the functions are differentiable and the graphs are concave up and concave down.
4. y=9/14x^(1/3)(x^2-7)
