Applications of Derivative

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7. Let a and b two positive numbers with 8a + 7b = 60 . Find the maximum value for their product, ab. 8. CBC is a right triangle with right angle C. This triangle's base is on the positive x-axis; the vertex 0 is at the origin, and the vertex C is on the positive x-axis. The vertex B is on the line 3! + 5x = 10. Find the maximum area of this triangle. Draw a diagram rst. 9. OBCD is a rectangle with corner 0 at the origin, corner B on the positive y-axis, corner D on the positive x-axis. The corner C is on the line 2y + 3x = 12. Find the maximum area of this rectangle. Draw a diagram rst. 10. 10. A box with a square base and closed top has a fixed surface area of 120 cm2. Find the dimensions of the box that give the maximum volume. 11. 1 1. An open box to be formed from a piece of metal 16 by 30 inches by cutting out squares of equal sides from the corners and bending up the sides. What size square should be cut out to create a box of greatest volume? What is the maximum volume? 12. Given f '(x) = (x2 +7) and f (1)=2, use differentials to estimate f (0.8). 13. Use differentials to approximate the change in the volume of a spherical balloon of radius 2 meters if the balloon deflates to a radius of 1.8 meters