Question
The first derivative of the function f is defined by \({f}'(x) = (x^2 +1)sin(3x – 1)\) for \(-1.5 < x < 1.5\). On which of the following intervals is the graph of f concave up?
A \((−1.5, −1.341)\) and \((−0.240, 0.964)\)
B \((−1.341, −0.240)\) and \((0.964, 1.5)\)
C \((−0.714, 0.333)\) and \((1.381, 1.5)\)
D \((−1.5, −0.714) and (0.333, 1.381)\)
Answer/Explanation
Question
The graph of y = ( fx) on the closed interval [2,7] is shown above. How many points of inflection does this graph have on this interval?
(A) One (B) Two (C) Three (D) Four (E) Five
Answer/Explanation
Ans:C
Question
Let f be the function given by\(f(x)=cosx(2x)+ln(3x)\). What is the least value of x at which the graph of f changes concavity?
(A) 0.56 (B) 0.93 (C) 1.18 (D) 2.38 (E) 2.44
Answer/Explanation
Ans:B
Question
At what value of x does the function \(y=1.2x^{2}-e^{.4x}\) change concavity?
(A) x = 2.5 ln 6
(B) x = 6 ln 2.4
(C) x = 2.4 ln 12
(D) x = 2.5 ln 15
Answer/Explanation
Ans:(D)
\(y’=2.4x-.4e^{.4x}\) \( y”=2.4-.16e^{.4x}\) The function can only change concavity when y ″ = 0
\(0=2.4-.16e^{.4x}\)
\(.16e^{.4x}=2.4\)
\(e^{.4x}=\frac{2.4}{.16}\)
\(e^{.4x}=15\)
\(0.4x=\ln 15\)