Question

Use a quick opproximation to estmate the derivative of the given function at the indeated polnt HadT.

F(x) = 3-3x ;x=2
f(2) =

Answer 1

To approximate the derivative of the function F(x) = 3-3x at x=2, we can use the concept of the difference quotient.

Step-by-step explanation:

To approximate the derivative of the function F(x) = 3-3x at x=2, we can use the concept of the difference quotient. The difference quotient represents the average rate of change of the function over a small interval. For small values of h, the difference quotient formula is:

f'(x) = (f(x+h) - f(x))/h

Let's calculate the derivative:

f'(x) = (f(2+h) - f(2))/h

Substituting the given function:

f'(x) = (3-3(2+h) - (3-3(2)))/h

Simplifying the expression gives:

f'(x) = -3

Therefore, the derivative of the function at x=2 is -3.