AP Calculus BC : 5.5 Using the Candidates Test to Determine Absolute (Global) Extrema- Exam Style questions with Answer- MCQ

Question

What is the absolute minimum value of y = −cos x − sin x on the closed interval \([0,\frac{\pi }{2}]\)?
A \(-2\sqrt{2}\)
B −2
C \(-\sqrt{2}\)
D −1

Answer/Explanation

 

Question

\(f(x)=\frac{1}{3}x^{3}-4x^{2}+12x-5 \)and the domain is the set of all x such that\(  0 \leq x\leq 9\), then the absolute maximum value of the function f occurs when x is
(A) 0                                      (B) 2                        (C) 4                                   (D) 6                                                        (E) 9

Answer/Explanation

Ans:E

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

Ans:A

 An equation of the line tangent to the graph of g at x=a is y=g(a)+g′(a)(x−a). In this question, a=−1. The value of y when x=−1.2 would be an approximation to g(−1.2).

Question

Let f be the function given by \(f(x)=x^{3}-6x^{2}-15x\). What is the maximum value of f on the interval [0,6]?

A 0

B 5

C 6

D 8

Answer/Explanation

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