Solve the below:
1. Find f(x), given that f'(x)=20x+3cos(x)
for all x and f(0)=2
2. Given that f is a differentiable function and the graph of its derivative is shown below, find the interval(s) in which f is decreasing.
![1502_graph of derivative.jpg](https://secure.tutorsglobe.com/CMSImages/1502_graph of derivative.jpg)
3. Find the critical numbers and the local extreme values of
f(x)=5x3/3+10x+1
a) Critical numbers are -2 and 2. Local Maximum at -2 and Local Minimum at 2.
b) No critical numbers and no local extrema.
c) Critical numbers are 2 and 0. Local Maximum at 2 and Local Minimum at 0.
d) Critical numbers are -2 and 0. Local Maximum at -2 and Local Minimum at 0.
e) Critical numbers are -2 and 2. Local Maximum at -2 and Local Minimum at 0.
4. Find the the local extreme values of
f(x)=2x2- 4/x4
a) Local Max: f(0) = 125, f(5) = 125; Local Min: f(-5) = 25
b) No local extrema.
c) Local Max: f(-5) = 125, f(5) = 125; Local Min: f(0) = 25
d) Local Max: f(-5) = 125; No Local Min
e) Local Max: f(-5) = 125; Local Min: f(0) = 25, f(5) = 25
f) None of the above.
5. Find the critical numbers of f(x)=2-5x/2+5x
a)No critical numbers.
b) -2/5, 0 and 2/5
c) -2/5 and 0
d) -2/5, 0 and 5
e) -5 and 5