Home / AP Calculus BC : 2.3 Estimating Derivatives  of a Function at a Point- Exam Style questions with Answer- MCQ

AP Calculus BC : 2.3 Estimating Derivatives  of a Function at a Point- Exam Style questions with Answer- MCQ

Question

Let f be the function given by \(f(x)=2^{x^{2}}\) . Selected values of f are given in the table above. If the values in the table are used to approximate f′(0.5), what is the difference between the approximation and the actual value of f′(0.5) ?
A 0
B 0.176
C 0.824
D 1

Answer/Explanation

Ans:B

Question

The graph of the trigonometric function f is shown above for a≤x≤b. At which of the following points on the graph of f could the instantaneous rate of change of f equal the average rate of change of f on the interval [a,b] ?

A A
B B
C C
D D

Answer/Explanation

Ans:B

Question

If \( f(x)=2+|x-3|\) all x, then the value of the derivative \(f'(x)at x=3 \)is
(A) -1                           (B) 0                                     (C) 1                              (D) 2                         (E) nonexistent

Answer/Explanation

Ans:E

 

Question

If \(y= In \left ( x^{2} +y^{2}\right )\)then the value of \(\frac{dy}{dx}\) at the point (1,0) is

(A) 0                                               (B)\(\frac{1}{2}\)                                        (C) 1                        (D) 2                              (E) undefined

Answer/Explanation

Ans:D

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