Find the value of the derivative of the function f(x) = 4√x at the given point (9,12).

Solution:

Derivatives are one of the most integral concepts of calculus which have many applications in various fields of engineering and science. Geometrically, it signifies the slope of a curve at a particular point. Let's solve an example related to the topic.

Let's understand the solution in detail.

We use the rules of differentiation to find the derivative of f(x) = 4√x

Hence, f'(x) = derivative of f(x) = 4 × 1/2 × x^-1/2 = 2 / √x

Now, we put the value of x-coordinate from the given point into the equation of f'(x).

Therefore, we get f'(9) = 2 / √9 = 2/3.

You can also check the answer using the derivatives calculator.

Hence, the value of the derivative of the function f(x) = 4√x at the given point (9,12) is 2/3.

Find the value of the derivative of the function f(x) = 4√x at the given point (9,12).

Summary:

The value of the derivative of the function f(x) = 4√x at the given point (9,12) is 2 / 3.