Question
Let f be the function defined by 
Which of the following statements about f is true?
(A) f is an odd function.
(B) f is discontinuous at x = 0 .
(C) f has a relative maximum.
(D)\( f ′(0) =0 \)
(E) \(f'(x) >0 \)for x ≠0
▶️Answer/Explanation
Ans:E
The only one that is true is E. A consideration of the graph of y = f(x), which is a standard cubic to the left of 0 and a line with slope 1 to the right of 0, shows the other options to be false.
Question
What is the minimum value of f(x ) ln x f ?
(A) −e (B) -1 (C) \(-\frac{1}{e}\) (D) 0 (E) f(x) has no minimum value.
▶️Answer/Explanation
Ans:C
Question
What is the area of the region in the first quadrant enclosed by the graphs of cos \(y=cosx, y=x,\)and the y-axis?
(A) 0.127 (B) 0.385 (C) 0.400 (D) 0.600 (E) 0.947
▶️Answer/Explanation
Ans:C
cosx =x at 0.739085. Store this in \(A\int_{0}^{A}(cosx-x)dx=0.400\)
Question
The first derivative of the function f is given by \(f'(x)=\frac{cos^{2}x}{x}-\frac{1}{5}\). How many critical values does f have on the open interval (0,10 ) ?
(A) One
(B) Three
(C) Four
(D) Five
(E) Seven
▶️Answer/Explanation
Ans:B
Look at the graph of ƒ'(x) on the interval (0,10) and count the number of x-intercepts in the interval.