Asked by mr maths
                find the gradient of the tangent to the parabola y=4x-x^2 at (0,0)
hence calculate the size of the angle between the line y=x and this tangent.
(as i cant show you the diagram all that it shows is the line going through (0,0) and having one point of contact)
            
        hence calculate the size of the angle between the line y=x and this tangent.
(as i cant show you the diagram all that it shows is the line going through (0,0) and having one point of contact)
Answers
                    Answered by
            Reiny
            
    This is a Calculus question.
dy/dx = 4 - 2x
at (0,) dy/dx = 4
so the slope or gradient of the tangent at (0,0) is 4
and the slope of y = x is 1
Did you know that the slope of a line is the same as the tangent of the angle that line makes with the x-axis?
so the line with slope of 4 makes an angle of 75.96º with the x-axis
the line y=x makes and angle of 45º with the x-axis
so the angle between them is (75.96-45)º
= 30.96º
    
dy/dx = 4 - 2x
at (0,) dy/dx = 4
so the slope or gradient of the tangent at (0,0) is 4
and the slope of y = x is 1
Did you know that the slope of a line is the same as the tangent of the angle that line makes with the x-axis?
so the line with slope of 4 makes an angle of 75.96º with the x-axis
the line y=x makes and angle of 45º with the x-axis
so the angle between them is (75.96-45)º
= 30.96º
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