Question

"Give an example of a function whose derivative is equals to 1

when x=2 and equals 4 evaluated at x=3 please give detailed working
and an explanation"

Answer 1

To find a function whose derivative is equal to 1 when x = 2 and equal to 4 when x = 3, we can use integration. The function is f(x) = x + 1.

Step-by-step explanation:

To find a function whose derivative is equal to 1 when x = 2 and equal to 4 when x = 3, we can use integration. Let's start by finding the antiderivative of the derivative 1, which is simply x. To ensure that the derivative equals 1 at x = 2, we add a constant, let's call it C1. So, the antiderivative is x + C1. Now, we need to find the value of C1. Using the given condition that the derivative is 4 at x = 3, we set up the equation x + C1 = 4 and solve for C1. Substituting x = 3, we have 3 + C1 = 4, which gives us C1 = 1. Therefore, the function whose derivative is equal to 1 at x = 2 and equal to 4 at x = 3 is f(x) = x + 1.