F(x) = 3 cos(x) 0 ≤ x ≤ 3π/4 evaluate the riemann sum with n = 6, taking the sample points to be left endpoints. (round your answer to six decimal places.)

Step-by-step explanation:

We want to find the Riemann sum for with n = 6, using left endpoints.

The Left Riemann Sum uses the left endpoints of a sub-interval:

where .

Step 1: Find

We have that

Therefore,

Step 2: Divide the interval into n = 6 sub-intervals of length

Step 3: Evaluate the function at the left endpoints

Step 4: Apply the Left Riemann Sum formula

answer: evaluate the objective function at each vertex to determine which - and -values, if any, maximize or minimize the function. example: find the minimum value and maximum value of the objective function f ( x , y ) = 4 x + 5 y , subject to the following constraints