5 Steps to a 5 AP Calculus BC 2019

AP Calculus BC Practice Exam 1 397

90. The correct answer is (D).

y

x

y (x)

(1, 4.5)

(^4) (0.5, 4)
y – 4 = x – 0.5
y = 4
01 0.5
Atx=0,
dy
dx
= 2 x=2(0)=0, which leads to a
horizontal tangent. Sincey(0)=4, the point of
tangency is (0, 4) and the equation of the
horizontal isy=4. A step size of 0.5 gives the
nextx-value atx= 0 .5, and you have the point
( 0 .5, 4), and
dy
dx
∣∣
∣∣
x= 0. 5
= 2 ( 0. 5 )=1. Thus, the
equation of the tangent at the point( 0 .5, 4)is
y− 4 = 1 (x− 0. 5 ).Atx=1,y− 4 = 1 ( 1 − 0. 5 )
ory= 4 .5. Thus,y( 1 )≈ 4 .5.