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