The function given is f(x)= x^3/4-sin x +1/2, interval=[0,2*pi]

a) plot the function over the interval to see its general behaviour.

f := x -> x^(3/4)-sin(x)+1/2;
plot(f(x), x=0..2*Pi);

b)FInd the interior points where f'=0.You may want to plot the f' as well.

d1:=D(f)(x);

plot (d1, x=0..2*Pi);

fsolve(d1=0, x);

       5.231279862

c) Find the interior points where f' does not exist.I don't know how to show question c) in Maple. Please help?   

When i do this,

d2:=solve(d1=infinity,x);
         

Is this the correct way to shoe f' does not exist? How to I get the numerical value of the RootOf....?

I wanted to have 3 graphs in 1 coordinate system. The Maple command I used was,

restart;
g := x -> (10*x)/(3+x);

f := x -> (10*x)/(5+x);

h := x -> (8*x)/(5+x);

plots:-display(
  plot( [g(x),f(x), h(x)], x=0..30, color=[red,blue, green], legend = ["k=3,c=10", "k=5, c=10","k=5,c=8"]));

Warning, unable to evaluate 1 of the 3 functions to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

The error comes up. only f(x) and h(x) were shown. How do I fix this? Thank you.

Monod Growth Model.

The function given was f(x)= cx/k+x , where c is the saturation value and k is the half-saturation constant.

I wanted to have the 2 graphs in 1 coordinate system, where both have c=5 but k= 2 and 3.

Is there also a way to clearly label and show that c=5 and extrapolate the point where k=2 and 3?

Thank you.

Size of a population is given by N(t) = 10 + 2e^-0.3t sin t, t>= 0

I tried to graph it using Maple but the highest and lowest point I got ( 11.3 and 9.5) was vastly different from the supposed answer of  4.421 and1.279 .

Please help! The Maple command I used was N := t -> 10 + 2*exp(-0.3*t)*sin(t);

Plus, is there any Maple command to show what the highest and lowest point of the graph is?

How do I get a graph from Maple for function f(x) that is continuous on [0,2] except at x=1, where f(1)=4, lim_{x approaching 1^-} f(x)=2, and lim_{x approaching 1⁺} f(x)=3?