Home / AP Calculus AB 4.6 Approximating Values of a Function Using Local Linearity and Linearization – MCQs

AP Calculus AB 4.6 Approximating Values of a Function Using Local Linearity and Linearization - MCQs - Exam Style Questions

AP Calculus AB-MCQs and Answers - All Topics

Calc-Ok Question

The function \(g\) is differentiable and satisfies \(g(-1)=4\) and \(g'(-1)=2\). What is the approximation of \(g(-1.2)\) using the line tangent to the graph of \(g\) at \(x=-1\) ?
(A) \(3.6\)  
(B) \(3.8\)  
(C) \(4.2\)  
(D) \(4.4\)
▶️ Answer/Explanation
Linearization at \(a=-1\): \(L(x)=g(a)+g'(a)(x-a)\).
Compute \(L(-1.2)=4+2(-1.2+1)=4-0.4=3.6\).
✅ Answer: (A)

No-Calc Question

Let \(f\) be a differentiable function such that \(f(2)=4\) and \(f'(2)=-\tfrac{1}{2}\). What is the approximation for \(f(2.1)\) found by using the line tangent to the graph of \(f\) at \(x=2\)?

(A) 2.95
(B) 3.95
(C) 4.05
(D) 4.1

▶️ Answer/Explanation

Equation of tangent: \(y-4=-\tfrac{1}{2}(x-2)\)
Simplify: \(y=-\tfrac{1}{2}x+5\)
Approximation: \(f(2.1)\approx -\tfrac{1}{2}(2.1)+5=3.95\)
✅ Answer: (B) 3.95

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