The slopes of the tangent lines to the graph of the function f(x) increase as x increases.
At what rate do the slopes of the tangent lines increase?
f(x) = x2 – 6
PLZZ help
To find the rate at which the slopes of the tangent lines increase, we need to find the derivative of the function f(x). The derivative will give us the rate of change of the function at any given point.
Let's find the derivative of the function f(x) = x^2 - 6 using the power rule of differentiation. The power rule states that for a function of the form f(x) = x^n, the derivative is given by f'(x) = n*x^(n-1).
In this case, n = 2:
f'(x) = 2 * x^(2-1)
= 2x
The derivative of the function is f'(x) = 2x.
Now, the slopes of the tangent lines at different points on the graph of f(x) are given by the derivative 2x. Since it is mentioned that the slopes of the tangent lines increase as x increases, it means that the derivative 2x is positive, given that x is positive.
Therefore, the rate at which the slopes of the tangent lines increase is given by the coefficient of x in the derivative, which is 2.