Differentiate and find the stationary point of the equation y = 7x^2 - 2x - 1.
First we will differentiate the equation.
To differentiate the equation we must multiply the coefficient by the power, and then subtract the power. If the is no x within an element the element becomes 0 when we differentiate.
7x2 -> 14x-2x -> -2 (When the coefficient has a minus sign we must remember to keep it.)-1 -> 0
So our differential is:
dy/dx = 14x - 2
Once we have differentiated the equation we must then find the stationary point.
To find the stationary point we must make dy/dx = 0 and then solve our new equation.
dy/dx = 14x-2
0 = 14x-2(add 2 to both sides)2 = 14x(divide both sides by 14)2/14 = x(we can simplify the left hand side)1/7 = x
Once we have found x, we must put x into the original equation to find y.
y = 7x2 -2x - 1
y = 7(1/7)2 - 2(1/7) - 1
y = -8/7
Once we have found y, we can put x and y together to find the stationary point.
Stationary point = (1/7, -8/7)
