Mathematics Homework Help

5.Consider the function ( )= ^4−4 ^3. Determine the following for f(x) , if they apply :I will be very picky about work shown. Do not use a calculator

.a)x- and y– intercepts :

b)Intervals on which f(x) increases and decreases:

c)Absolute and relative maxima and minima:

d)Intervals of concavity:

e)Points of inflection:

f)Sketch = ( ) using the above information.

6.Use the definition of the definite integral (this involves a limit) to evaluate ∫3,1(x^2+1) . Use the Fundamental Theorem of Calculus to check your answer. Show all the steps.

7.Set up a definite integral that gives the area of the region between the graphs of ( )= ^2+2 +1 and ( )=2 +5. Sketch and shade the region. Then use your calculator to solve the integral.