Question

Let f be a differentiable function with f(2) = 3 and f'(2) = -5.

A. Find f(3)
B. Find f'(3)
C. Determine f''(2)
D. Evaluate f''(3)

Answer 1

To find the value of f(3), we need to use the given information about the function f and its derivative. Since f is differentiable and its derivative at x = 2 is -5, we can estimate the value of f(3) based on the slope of the tangent line at x = 2.

Step-by-step explanation:

To find the value of f(3), we need to use the given information about the function f. Since we know that f is differentiable, we can use the derivative of f to find its value at different points. The derivative of a function represents its rate of change.

Given that f'(2) = -5, the derivative of f at x = 2 is -5. This means that the slope of the tangent line to the graph of f at x = 2 is -5.

Since the function f is differentiable, we can use this information to estimate the value of f(3). Since the slope of the tangent line at x = 2 is negative, we can assume that the graph of f is decreasing around this point. Therefore, we can estimate that f(3) will be less than f(2). However, without more information about the shape of the graph, we cannot determine the exact value of f(3).