AP Calculus BC 2.2 Defining the Derivative of a Function and Using Derivative Notation - Exam Style Questions - MCQs - New Syllabus
Calc-Ok Question
Let \(f\) be a differentiable function. The figure shows the line tangent to the graph of \(f\) at \(x=0\). Of the following, which must be true?
(A) \(f'(0)=-f(0)\)
(B) \(f'(0)<f(0)\)
(C) \(f'(0)=f(0)\)
(D) \(f'(0)>f(0)\)
(B) \(f'(0)<f(0)\)
(C) \(f'(0)=f(0)\)
(D) \(f'(0)>f(0)\)
▶️ Answer/Explanation
Detailed solution
The tangent line at \(x=0\) has:
- slope \(= f'(0)\)
- y-intercept \(= f(0)\) (since the tangent line passes through \((0, f(0))\))
From the graph, the tangent line’s y-intercept equals its slope (both negative with the same magnitude), so \(f'(0)=f(0)\).
✅ Answer: (C)