5 Steps to a 5 AP Calculus AB 2019 - William Ma

MA 3972-MA-Book April 11, 2018 16:32

358 STEP 5. Build Your Test-Taking Confidence

• 4 – 2
  
  
  • 10 1
  
  
  
  

1.5 2

Graph of f ́

y

C

A

B x

5. A functionfis continuous and twice
   differentiable for all values ofx. The figure
   above shows the graph off′, the derivative of
   functionfon the closed interval [−4, 2]. The
   graph off′has horizontal tangents atx=− 1
   andx= 1 .5. The areas of regionsA,B, andC
   are 20, 10, and 6, respectively, andf(2)=3.
   (A) Find allx-values on (−4, 2) such that the
   functionf has a local minimum. Justify
   your answer.
   (B) Find all x-values on (−4, 2) such that
   the graph of f has a point of inflection.
   Justify your answer.
   (C) Evaluate lim
   x→ 1

2 f(x)

x+ 1

. Explain your reason-
ing.
(D) Evaluate lim
x→− 2

f(x)+ 1

x+ 2

. Explain your
reasoning.
6. The equation of a curve is given as
14 y−y^2 =x^2 +24.

(A) Find

dy

dx

in terms ofxandy.

(B) Write an equation of the line tangent to

the curve at the point (−3, 11).

(C) Write an equation of each vertical tangent

to the curve.

(D) Evaluate

d^2 y

dx^2

at the point (0, 2).

STOP. End of AP Calculus AB Practice Exam, Section II Part B.