MATH 225 WEEK 2 TEST | QUESTIONS AND ANSWERS | 2026 UPDATE | 100% CORRECT.

MATH 225 WEEK 2 TEST | QUESTIONS AND ANSWERS | 2026 UPDATE |
100% CORRECT.



Question1 cn




Find the derivative of:
cv cv cv




3
h(x)= x +3x+4.
x3+35x−2 4
cv
cn




6x +18x +6x 3+6x 2 +18x +6
cv cn



c n c n c n cv




h'(x)=
2
x3+3x−2 ( cn
)
3 2
h'(x)=18x +6x +18x+6
2
x3+3x−2 ( )
h'(x)= −18x2 −18 cv




2
x3+3x−2 ( )
h'(x)= 6x2+6 cn
cn
cn




(x3+3x−2)2 cn
cn cn cn




Question2 cn




Find the derivative.
cv cv




f(x)=2πx2
cn cn cn




f′(x)=4πx
cn




f′(x)=2πx
cn
cn

cn cn




f′(x)=4πx2 cv




f′(x)=3.14


Question3 cn




Supposef(x)=−x−1.Whatistheslopeofthelinetangenttofatx =3?
cv
n
c
cv
n
c
cv cv
cn cn cn
cv
cn c n 1

−1
cn




0
cn




1
9

, Question4 cn




Givenf(x)=x2 +x,whatistheslopeofthe lineta nge
cv cv cv cv cv cn cn




nt tof(x) atthepoint (2, 6)?
cv cn cn c n cn cn c n c n




m= 5 cn cn




m= 6 cn cn




m= 3 cn cn




m= 4 cn cn




Question5 cn




Suppose f(x)=−x2+2. cv




Whatistheequationofthelinetangenttoth e curve
cv cv cv cv cv cn cn cv




wi9th a slopeequalto 1? cn cv




y=x+
4
cn




y=x+ 5
cn




4
c n




y=x− 5
cn c n




4
y=x−
cn
9 c n




4


Question6 cn




Isthefunctionf(x)=
x+3 differentiable
cn cn cn cn




x2 c n




o
nthe openinterval(−4,4)? cv




Yes,thefunction is differentiable on that interval. cn cn cv cn cn cv




No, the function is not differentiable on that interval.
cn cn cn cn cn cn cn cv




Question7 cn




Findtheequationofthesecant line tot
cv cv cv c




hecurvef(x)=3x2−2onthe interval
n cv
cv

cv cn cn




[1.9, 2.1]. cn




y= 12x − 13.97 cv cn cn




y=24x−39.17 cn cn




y=12x−36.43 cn cn




y=24x −61.63
nc cn cn cn cn