Complete the definition of the Intermediate Value Theorem
If f is continuous on [a,b] and k is any # between f(a) and f(b), then there is at least one number c in [a,b] s.t.
What is f(c)=k
100
d/dx [arctan(2x)].....
What is 2/(1+4x2)?
200
Find the derivative of 7x3+9x2+5x
What is 21x2+18x+5?
200
Find the derivative of f(x)=ln(x3+3x2+7).
What is (3x2+6x)/(x3+3x2+7)?
200
Integrate F'(x) = x2
What is (x3/3 +C
200
What does the Mean Value Theorem state?
What is there exists a point c in the interval (a,b) such that f'(c)=f(b)-f(a)/b-a, if a function is continuous on the closed interval [a,b] and differential on the open interval (a,b)?
200
Volume formula of a cone
What is (1/3)pi h r2
300
Find the slope of f(x)=5/3x3-3x2-1/x2 at x=-1
What is 9?
300
Find dy/dx for the following function: x2y3+y2+3x=y.
What is (-3-2xy3)/(3x2y2+2y-1)?
300
Find the equation of F given F'(x)=x3-3x2+7x+8 and F(0)=5
What is F(x)=(x4/4)-x3+3.5x2+8x+5
300
Find a value c such that the conclusion of the mean value theorem is satisfied for f(x)=2x,3+6x-2 on the interval [-2,2].
What is ± 2/(3).5?
300
The rate of change of radius r of a circle is 4 cm/s. Find the rate of change of Area A when r=2cm.
What is 16π?
400
Find the derivative of f(x)=(x+3)3/(x-2)2-x2(7x+7)
What is (x+3)2[3(x-2)-2(x+3)]/(x-2)3-21x2-14x?
400
Find the derivative of f(x)=tan(3x).
What is 3sec2(3x)
400
Solve for y=f(x) when f(3)=2.
dy/dx=x2+3x/y2
What is (2/3x3+2x2-32).5?
400
What is the limit definition of the derivative?
limit as delta x approaches 0 of "f of x plus delta x' minus f of x' all over delta x'
400
The acceleration of a particle is given by the function a(t)=3t2+7. Find the position function of the particle given that its initial velocity is 10 m/sec and an initial height of 80m.
What is s(t)=(t4/4)+3.5t2+10t+80?
500
Find the derivative of f(x)=3x2+7x-2 using the limit process.
What is 6x+7?
500
Solve for d2y/dx2 when y2=3x2+4x+y at the point (2,5).
What is -.036?
500
Integrate x/(4+x2).5.
What is (4+x2).5+C?
500
Definition of a critical number states: ' Let f be defined at c if....