#Calculate the first derivative of the following functions:# 2*x^4 + 3*x^2 + 2*x + 7f(x)=3*x^6-2*x^4+3*x^2+2*x+7diff(f(x),x)
18*x^5 - 8*x^3 + 6*x + 2
#Graph the second and fourth derivative from the function abovef(x)=3*x^6-2*x^4+3*x^2+2*x+7diff(f(x),x,2)diff(f(x),x,4)
90*x^4 - 24*x^2 + 6
1080*x^2 - 48
#Graph 2*sin(2*x) and its derivative on a graph, using two different colors to represent the different functionsf(x)=2*sin(2*x)g(x)=diff(f(x),x)plot(f(x),-pi,pi)+plot(g(x),-pi,pi,color='red')
90*x^4 - 24*x^2 + 6
1080*x^2 - 48
#Find the point of intersections between 0 and pif(x)=2*sin(2*x)g(x)=diff(f(x),x)find_root(f(x)==g(x),0,pi/2)
0.5535743588970452
find_root(f(x)==g(x),pi/2,pi)
2.1243706856922784
#Graph the points of intersectiona=0.5535743588970452b=2.1243706856922784f(x)=2*sin(2*x)g(x)=diff(f(x),x)f(a)