Calculus UNIT306 What's Implicit Differentiation?

2778 days ago by MATH4R2013

#1) x^2+y^2==10, find dy/dt 
       
#2) (x-h)^2+(y-k)^2==r^2, find dy/dx 
       
#91AB3) f(x)=(1+tan(x))^(3/2) find tangent line at x=0 f(x)=(1+tan(x))^(3/2) g(x)=diff(f(x),x) show(f(x)) show(g(x)) show(f(0)) show(g(0)) h(x)=(3/2)*(x-0)+1 p1=plot(f(x),-pi/4,pi/4,color='red') p2=plot(h(x),-pi/4,pi/4,color='green') p1+p2 
       




#80AB5a) f(x)=cos(x)-cos(x)^2 0<=x<=pi find the x-intercepts, y-intercepts f(x)=cos(x)-cos(x)^2 show(solve(f(x)==0,x)) show(f(0)) 
       

#80AB5b) f(x)=cos(x)-cos(x)^2 0<=x<=pi find any absolute minimums or maximums g(x)=diff(f(x),x) show(g(x)) show(solve(g(x)==0,x)) 
       

show(f(0)) show(f(pi/3)) show(f(pi)) 
       


plot(f(x),0,pi)