Evaluate , and tell whether its antiderivative F is increasing or decreasing at the point radians.
A)-0.288, increasing
B)0.757, increasing
C) -0.757, decreasing
D)0.277, decreasing
E)0.757, decreasing

Question

Evaluate  , and tell whether its antiderivative F is increasing or decreasing at the point  radians.
A)-0.288, increasing 
B)0.757, increasing 
C) -0.757, decreasing 
D)0.277, decreasing 
E)0.757, decreasing

Quizplus · Accepted Answer

This question requires us to evaluate the given expression and determine whether its antiderivative is increasing or decreasing at a certain point. Using the power rule of integration, we can find that the antiderivative of 11eaa3e5_55b3_3eba_9f8f_bdc1329d08bd_TB5971_11 is -cos(11eaa3e5_55b3_3eba_9f8f_bdc1329d08bd_TB5971_11), plus a constant of integration.

To determine whether this antiderivative is increasing or decreasing at 11eaa3e5_55b3_3ebb_9f8f_abc2a95a47c5_TB5971_11 radians, we need to look at the derivative of -cos(11eaa3e5_55b3_3eba_9f8f_bdc1329d08bd_TB5971_11). Using the chain rule, we find that the derivative is sin(11eaa3e5_55b3_3eba_9f8f_bdc1329d08bd_TB5971_11), which is negative at 11eaa3e5_55b3_3ebb_9f8f_abc2a95a47c5_TB5971_11 radians. Therefore, the antiderivative is decreasing at this point, and the answer is C.

Evaluate , and Tell Whether Its Antiderivative F Is