Derivatives
What is the derivative of 6x3+4
18x2
Find the integral of (4x-6)dx
2x2-6x+C
How do you find the are between 2 curves?
integral of (upper curve- lower curve)dx
Find the volume of the solid generated by the region bounded by the graphs of the equations f(x)=5, g(x)=x2
40sqrt(5)pi
d/dx (f(x) g(x)) = f(x)g'(x) + g(x) f'(x)
Product Rule
What is the derivative of (9x2)(14x)
378x2
Find the integral of (csc2 x)dx
-cot(x)+C
Find the area between f(x)=x3 and g(x)=7+x
8.369
Find the volume of the solid generated by the region bounded by the graphs of the equations f(x)=6x2, g(x)=0
36pi/5
f'(c)= f(b)-f(a)/ b-a
Mean Value Theorem
What is the derivative of (8x5)/(11x3)
11/4x3
Find the integral of by using substitution of ((3+5x)3)(2)dx
1/10((3+5x)4)+C
Find the area between f(x)= x3-5x+2 and g(x)=0
13.721
Find the volume of the solid generated by the region bounded by the graphs of the equations f(x)= sin(x) , g(x)=x^2
6143.580
g'(x) = 1/ f'(g(x)) where g(x) is the inverse of f(x)
Derivative of an Inverse Function
What is the derivative of (sinx2)
2x cos(x2)
Find the integral of by using substitution of x2(x3+2)dx from -1 to 1
4/3
Find the area between f(x)= x2+3x+2 and g(x)=3x+7
14.907
Find the volume of the solid generated by the region bounded by the graphs of the equations f(x)=(4x+5)2 , g(x)= 11x
41338pi/15 or 8657.810
If f is continuous on the closed interval [a,b] and k is any number between f(a) and f(b) then there is at least one number c in [a, b] such that f(c) = k
Intermediate Value Theorem
What is the derivative of (tanx2)(6x3)
12x4 sec2(x2)+18x2tan(x2)
Find the integral of by using substitution of (6x3+2x2-3x)dx, from -1 to 3
380/3
Find the area between f(x)=xe(-3x), y=0
0.089
Find the volume of the solid generated by the region bounded by the graphs of the equations f(x)=sinx2 , g(x)=3xe2-6x
67885.543
If f is continuous on the closed interval [a, b], then f has both a maximum and a minimum on the interval.
Extrema Vale Theorem