What do you mean by "given by"? We are told that the tangent line is y= x+ 1. The derivative of the curve is the slope of the tangent line, which is 1.arunbg said:Hmm, according to the question the slope at point (2,3) is already given by y=x+1(correct me if my interpretation is wrong).
The concept of finding f'(2) involves using the derivative of a function to find the slope of the tangent line at a specific point, in this case, the point (2, f(2)).
f'(2) is calculated by taking the limit as x approaches 2 of the function f(x) - f(2) divided by x - 2. This is known as the derivative definition and is represented mathematically as f'(2) = lim(x→2) (f(x) - f(2)) / (x - 2).
Finding f'(2) is important because it allows us to determine the slope of the tangent line at a specific point on a curve. This information can be used in various applications, such as optimization problems and curve sketching.
Yes, f'(2) can be undefined if the function f(x) is not differentiable at x = 2. This could happen if the function is not continuous or has a sharp turn at x = 2.
Finding f'(2) can be applied in real-world scenarios such as determining the maximum or minimum value of a function, finding the rate of change of a quantity, or determining the direction of movement of an object.