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

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


Question 1 cv




Find the derivative of:cv cv cv




3
h(x)= x 3+3x+4.
cv

cv cv cv cv




x +35x −2 4
cv c v




3 2
cv
cv cv cv c v




6x +18x +6x +6x +18x+6 c v cv c v cv c v cv cv cv cv




h'(x)=
2
cv cv cv




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

cv cv cv cv




2
cv cv cv cv




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




2
cv cv cv




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




(x3 + 3x − 2)2 cv
cv cv cv




Question 2 cv




Findthe derivative. cv cv




f (x) = 2πx2
cv cv cv




f′(x) = 4πx
cv cv
cv
cv cv




f′ (x) = 2πx
cv cv
cv

cv cv




f′(x)=4πx2
cv cv
cv

cv cv




f′(x) = 3.14
cv cv
cv

cv cv




Question 3 cv




Suppose f (x) = −x−1. What is the slope of the line tangent to f at x = 3?
cv cv cv cv v
c cv cv cv cv cv cv cv cv cv cv cv cv cv cv cv 1
cv




cv −1
cv 0
1
9

, Question 4 cv




Givenf(x)=x2 +x,whatistheslopeofthe line ta cv cv cv cv
cv

cv cv cv cv cv cv cv cv cv




ngent to f (x) at the point (2, 6)? cv cv cv c v cv cv c v c v




cv m=5 cv cv




cv m=6 cv cv




cv m=3 cv cv




cv m=4 cv cv




Question 5 cv




Suppose f(x)=−x2+2. cv cv cv cv
cv

cv




Whatistheequationofthelinetangent to th cv cv cv cv cv cv cv cv cv




e curve with a slope equal to 1?
y= x + 9
cv cv cv cv cv cv cv




4
cv cv cv c v




y= x + 5
4
cv cv cv c v




y= x− 5 cv cv cv c v




4
cv




y= x− 9
cv cv cv cv c v




4


Question 6 cv




Is the function f(x) =
x+3 differentiable
cv cv cv cv




x2 o
cv cv


cv




ntheopeninterval(−4,4)?
cv cv cv cv cv




Yes, the function is differentiable on that interval.
cv cv cv cv cv cv cv cv




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




Question 7 cv




Findtheequationofthe secantline tot
cv cv cv cv cv cv cv cv




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

cv cv cv cv c




[1.9, 2.1] .
v c v cv




y = 12x − 13.97
cv cv cv cv cv




y = 24x − 39.17
cv cv cv cv cv




y = 12x − 36.43
cv cv cv cv cv




cv y = 24x − 61.63
cv cv cv cv