Use the mean value theorem to solve the following result: Let f(x) be continuous at 'a' and suppose the limit x→a f'(x) exists. Then f(x) is differentiable at a and f'(a) = lim→a f'(x)

Jackie bought a bag of oranges. she used 3/8 of the oranges to make orange juice. she used 1/3 of the oranges to make a fruit salad. she put 1/8 of the oranges in a bowl on the table. she put 2/12 of the oranges in the refrigerator. a) jackie left more oranges on the table than she put in the refrigerator. b) jackie used fewer oranges to make orange juice than she left on the table. c) jackie put fewer oranges in the refrigerator than she used to make the fruit salad. eliminate d) jackie used more oranges to make a fruit salad than she used to make orange juice.

Find the coordinates of point x that lies along the directed line segment from y(-8, 8) to t(-15, -13) and partitions the segment in the ratio of 5: 2.

Kevin's bank offered him a 4.5% interest rate for his mortgage. if he purchases 3 points, what will be his new rate?