-2 -1 3 pove function f(x ) = 2 1.2", estimate f'(x) using h = 0.001 for the following three val

Find the interval where the function is increasing. Find the interval where the function is decreasing. Step 1 If f(x) = then f '(x) = (x² – 4)'

The size of a population of butterflies is given by the function. p(t)= 6000/(1+49(0.6)t) where t is the time in days. Determine the rate of growth in the population after 5 days using derivative, and verify graphicallyusing technology.

Differentiate the function.

A large tank has a capacity of 300 gallons. Initially, the tank contains a brine solution of 200 gallons with 40 pounds of dissolved salt. A solution with a concentration of 4 pounds of salt per gallon is admitted into the tank and the well-stirred solution is withdrawn from the tank at a rate of 2 gallons per minute. a) Find the function (1) where y(1) represents the number of pounds of salt in the tank at f minutes. Give exact values here. b) Find the number of pounds of salt in the tank when the tank is completely full. Express your answer as a decimal with 1 decimal place accuracy.

ƒf'(x) 6 3 X 8 Write down the value(s) of x for which the original function y = f(x) is a. Stationary. b. Increasing. c. Concave down. d. Has a point of inflection.

The approximate rate of change in the number of design patent applications received in recent years is given by the equation below, where t represents the number of years since 2000 and p represents the number of design patents (in thousands). In 2017, the number of applications for a design patent was 43,340. p'(t) = 0.01021t+2.03 Complete parts (a) and (b) below. (a) Find the function that gives the total number (in thousands) of design patent applications received in year t. p(t) = (Type an exact answer.)