I learned that integrals are finding the area under a curve. But I seem to be a little confused. Area under the curve of the derivative of the function? Or area under the curve of the original function?
If an integral is the area under a curve, why do we even have to find the anti derivative...
1. Homework Statement
Let A be a set of critical points of the function f(x).
Let B be a set of roots of the equation f''(x)=0.
Let C be a set of points where f''(x) does not exist.
It follows that B∪C=D is a set of potential inflection points of f(x).
Q 1: Can there exist any inflection...
1. Homework Statement
1) I am having trouble with the questions, "Use the logarithmic derivative to find y' when y=((e^-x)cos^2x)/((x^2)+x+1)
2. Homework Equations
(dy/dx)(e^x) = e^x
(dy/dx)ln(e^-x) = -x ?
3. The Attempt at a Solution
First I believe I put ln on each set of terms (Though I...
1. Homework Statement
The revenue function for a product is r = 8x where r is in dollars and x is the number of units sold. the demand function is q = -1/4p + 10000 where q units can be sold when selling price is p. what is dr/dp?
2. Homework Equations
r=pq
3. The Attempt at a Solution
I...
1. Homework Statement
Show that if F is an antiderivative of f on [a,b] and c is in (a,b), then f cannot have a jump or removable discontinuity at c. Hint: assume that it does and show that either F'(c) does not exist or F'(c) does not equal f(c).
2. The attempt at a solution
I attempted a...
Hi,
So I'm working through a bunch of problems involving gradient vectors and derivatives to try to better understand it all, and one specific thing is giving me trouble.
I have a general function that defines a change in Temperature with respect to position (x,y). So for example, dT/dt would...
1. Homework Statement
A police car is parked 50 feet away from a wall. The police car siren spins at 30 revolutions per minute. What is the velocity the light moves through the wall when the beam forms angles of: a) α= 30°, b) α=60°, and c) α=70°?
This is the diagram...
1. Homework Statement
Suppose a can, after an initial kick, moves up along a smooth hill of ice. Make a statement concerning its acceleration.
A) It will travel at constant velocity with zero acceleration.
B) It will have a constant acceleration up the hill, but a different constant...