Let f be the function defined by f(x) = x + lnx. what is the value of c for which the instantaneous rate of change of f at x = c is the same as the average rate of change of f over [1, 4]?

Ineed big ! the cost of a school banquet is $25 plus $15 for each person attending. create a table, sketch the graph, and write an equation in slope-intercept and point-slope form that gives total cost as a function of the number of people attending. what is the cost for 77 people?

Abucket of paint has spilled on a tile floor. the paint flow can be expressed with the function p(t) = 6(t), where t represents time in minutes and p represents how far the paint is spreading. the flowing paint is creating a circular pattern on the tile. the area of the pattern can be expressed as a(p) = 3.14(p)^2 part a: find the area of the circle of spilled paint as a function of time, or a[p(t)]. show your work. part b: how large is the area of spilled paint after 8 minutes? you may use 3.14 to approximate pi in this problem.

Astocks price gained 3% in april and 5% in may and then lost 4% in june and 1% in july during which month did the stocks price change the most