Problem 9 - Calculus Early Transcendentals

Question

If \(F(x)=x^{2}-3 x+C\) and \(F(-1)=4,\) what is the value of \(C ?\)

Step-by-Step Solution

Answer

Answer: The value of C is 0.

Step 1: Substitute x = -1 into the function

Plug in \(x = -1\) into the function \(F(x) = x^2 - 3x + C\): \(F(-1) = (-1)^2 - 3(-1) + C\).

Step 2: Solve for C

Next, we use the given information that \(F(-1) = 4\) and substitute this into the equation: \(4 = (-1)^2 - 3(-1) + C\).

Step 3: Simplify the equation

Simplify the equation: \(4 = 1 + 3 + C\).

Step 4: Calculate the value of C

Rearrange the equation to find the value of \(C\): \(C = 4 - 1 - 3\).

Step 5: Write the final answer

Finally, we find the value of \(C\): \(C = 0\)