Answer:
(3, - 9)
Step-by-step explanation:
Differentiate using the power rule
y = a[tex]x^{n}[/tex] , then
[tex]\frac{dy}{dx}[/tex] = na[tex]x^{n-1}[/tex]
Given
y = x² - 6x
[tex]\frac{dy}{dx}[/tex] = 2x - 6
Equate to zero since the measure of gradient is [tex]\frac{dy}{dx}[/tex] , that is
2x - 6 = 0 ( add 6 to both sides )
2x = 6 ( divide both sides by 2 )
x = 3
Substitute x = 3 into y for corresponding value of y
y = 3² - 6(3) = 9 - 18 = - 9, thus
(3, - 9 ) are the coordinates of the point where the gradient is zero
