0
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.
Add your answer:
Earn +20 pts
How do you find the slope of a graph if it is a curve?
You find the slope of the tangent to the curve at the point of interest.
How do you find the slope of an Indifference curve?
You find the tangent to the curve at the point of interest and then find the slope of the tangent.
What is the smallest slope on the curve?
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.
The derivative finds the of a curve?
The gradient of the tangents to the curve.
How the slope of a curved line at a point can be found?
The slope of a curved line at a point is the slope of the tangent to the curve at that point. If you know the equation of the curve and the curve is well behaved, you can find the derivative of the equation of the curve. The value of the derivative, at the point in question, is the slope of the curved line at that point.
What is the slope of a curve?
Slope of a Curve A number which is used to indicate the steepness of a curve at a particular point.The slope of a curve at a point is defined to be the slope of the tangent line. Thus the slope of a curve at a point is found using the derivative
How do you find the slope of the tangent line to each curve at the given point?
By differentiating the answer and plugging in the x value along the curve, you are finding the exact slope of the curve at that point. In effect, this would be the slope of the tangent line, as a tangent line only intersects another at one point. To find the equation of a tangent line to a curve, use the point slope form (y-y1)=m(x-x1), m being the slope. Use the differential to find the slope and use the point on the curve to plug in for (x1, y1).
What determines the slope of IS Curve?
mainly the slope of Is curve depends on ; -the slope of investment schedule -the size of the multiplier
Is the price elasticity constant along the demand curve?
Price elasticity of demand is equal to the instantaneous slope of the demand curve, or the slope of the tangent line at any point on the demand curve. So if the demand curve is represented by a straight downward sloping line, then yes, price elasticity of demand is equal to the slope of the demand curve. Otherwise, the slope at any point on the curve is changing, and you can find the it by taking the derivative of the demand curve function, which will find the Price elasticity of demand at any single point. Thus, the Price Elasticity of Demand changes at different points on the demand curve.
What is a slope line?
is it a line that is slanted
How do you find modulus of elasticity from load displacement curve?
The modulus of elasticity is the slope of the linear portion of the curve (the elastic region).
How do you calculate slope of a curve?
If the curve is on the xy-plane, finding an expression for dy/dx will give you the slope of a curve at a point.
