Calculus UNIT204 HWK p105 #25

2812 days ago by MATH4R2013

#25) which function is it's own derivative?
a) y=sin(x)
b) y=x
c) y=sqrt(x)
d) y=e^x=exp(x)
e) y=2*x

[see notes below!]



#25a) p105 var('h') f(x)=sin(x) g(x)=diff(f(x),x) show(f(x)) show(g(x)) p1=plot(f(x),0,2*pi,color='red') p2=plot(g(x),0,2*pi,color='green') (p1+p2).show(aspect_ratio=1) 
       


#25b) p105 var('h') f(x)=(x) g(x)=diff(f(x),x) show(f(x)) show(g(x)) p1=plot(f(x),0,10,color='red') p2=plot(g(x),0,10,color='green') (p1+p2).show(aspect_ratio=1) 
       


#25c) p105 var('h') f(x)=sqrt(x) g(x)=diff(f(x),x) show(f(x)) show(g(x)) p1=plot(f(x),0,10,color='red') p2=plot(g(x),0,10,color='green') (p1+p2).show(aspect_ratio=1) 
       


#25d) p105 var('h') f(x)=exp(x) g(x)=diff(f(x),x) show(f(x)) show(g(x)) p1=plot(f(x),0,1,color='red') p2=plot(g(x),0,1,color='green') (p1+p2).show(aspect_ratio=1) 
       


#25d) p105 var('h') f(x)=x^2 g(x)=diff(f(x),x) show(f(x)) show(g(x)) p1=plot(f(x),-1,1,color='red') p2=plot(g(x),-1,1,color='green') (p1+p2).show(aspect_ratio=1) 
       


NOTES:

Green curves above are all derivative functions of the red functions.

When the green curve is positive, the red curve is increasing.

When the green curve is negative, the red curve is decreasing.

When the green curve is zero, the red curve has a min or a max.

f(x)=e^x is it's own derivative!