How do you find the smallest slope of a curve?

Answer 1

Well, honey, to find the smallest slope of a curve, you need to locate the point where the derivative is equal to zero. That's where the curve is either at a local minimum or maximum, so the slope is at its smallest. So, put on your detective hat and start solving those derivatives to track down that pesky little slope.

Answer 2

Oh, dude, finding the smallest slope of a curve is like finding the least exciting flavor at an ice cream shop. You just take the derivative of the function, set it equal to zero to find the critical points, and then plug those into the second derivative test to see which one gives you the smallest slope. It's as thrilling as watching paint dry!

Answer 3

The smallest slope of a curve means the point at which the derivative (the slope) is minimal. So find the derivative first, then find the minimum value of this function. That means finding another derivative and setting it equal to zero to solve for x. Example with the curve y = x^3 - x^2 : The slope at any given point is given by the derivative, which is 3x^2 - 2x. To find the minimum value of this function, compute its derivative (which is 6x - 2) and set it equal to zero. Solve 6x - 2 = 0 for x and you'll find the answer. It's x = 1/3. This is the point at which the smallest slope occurs. The smallest slope ITSELF is the value of the first derivative at x = 1/3, so plug x = 1/3 into 3x^2 - 2x and you get -1/3. This method could also have found the LARGEST slope of the initial curve. So you have to make sure by computing the slope at another point (any other point). Take x = 0. There the slope is 0, which is bigger than -1/3. So the -1/3 value is indeed the SMALLEST slope.