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pip_beard
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Homework Statement
gradient of the stationary points of y=1-2sinx domain 0<x<2pi
Homework Equations
The Attempt at a Solution
dy/dx = -2cosx
-2cosx=0...?
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rock.freak667 said:Gradient of the stationary point? Do you need to find that or the gradient? Because when you put dy/dx=0 it sort of implies what the gradient will be.
pip_beard said:Sorry. the qu reads 'the curve y=1-2sinx has domain 0<x<pi. find the gradients of the curve at the points where the curve crosses the x-axis
pip_beard said:so do i differentiate it and make it = 0?
so i get -2cosx=0
pip_beard said:so do i differentiate it and make it = 0?
so i get -2cosx=0
pip_beard said:how to i rearrange this to work it out?
pip_beard said:-2sinx=1
sinx=-1/2
pip_beard said:-2sinx=1
sinx=-1/2
pip_beard said:principle value of -0.523 (but out of range) the pi-(-0.523) = 3.6651
therfore value = 3.6651 and 6.2832?
pip_beard said:ohhh... did sin^-1... so ...
x principle = 0.479425
so pi - 0.4879425 = 2.66216
The gradient of a stationary point is the slope or rate of change of a function at that particular point. It indicates the direction and steepness of the function at the point where it is neither increasing nor decreasing.
To calculate the gradient of a stationary point, you need to take the derivative of the function at that point. This can be done by using the derivative rules such as the power rule, product rule, or chain rule depending on the form of the function.
A positive gradient at a stationary point indicates that the function is increasing at that point. This means that as you move along the function in the positive direction, the function values will also increase.
To determine if a stationary point is a maximum or minimum, you can use the second derivative test. If the second derivative is positive, then the stationary point is a minimum. If the second derivative is negative, then the stationary point is a maximum. If the second derivative is zero, then the test is inconclusive.
Yes, a stationary point can have a zero gradient. This means that the function has a horizontal tangent at that point, and the function values are neither increasing nor decreasing at that point. In this case, the stationary point can be a maximum, minimum, or a point of inflection.