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