Apentix/AP Calculus AB/Unit 4: Contextual Applications of Differentiation/Question

AP Calculus ABmediummcq1 pt

Use the tangent line to $f(x)=\sqrt{x}$ at $x=4$ to approximate $\sqrt{4.2}$ .

A.

2.2

B.

2.1

C.

2.025

D.

2.05

Explanation

Core Concept

The tangent line is $L(x)=f(4)+f'(4)(x-4)=2+\dfrac{1}{4}(x-4)$ . Substituting $x=4.2$ gives $2+\dfrac{0.2}{4}=2.05$ .

Correct Answer

D $2.05$

More Unit 4: Contextual Applications of Differentiation practice questions

hardAt noon, ship A is 100 km west of ship B. Ship A sails east at 20 km/h and ship B sails north at 15 km/h. How fast is the distance between t…
hardWater drains from an inverted conical tank 10 m tall with a top radius of 5 m at a rate of 2 m$^3$/min. How fast is the depth of the water d…
hardWhat is $\displaystyle\lim_{x\to\infty}\dfrac{x^3}{e^x}$?
hardWhat is $\displaystyle\lim_{x\to 0}\dfrac{1-\cos x}{x^2}$?
hardWhat is $\displaystyle\lim_{x\to 0}\dfrac{e^x-1-x}{x^2}$?

Try a random question →

Practice more AP Calculus AB questions with full explanations

Practice Unit 4: Contextual Applications of Differentiation Questions →