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Quiz

Lesson 1 Quiz: Rate of Change and Differentiation Rules

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  • Questions count: 10
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1.
The derivative of f(x) = 4 x3 - 5 x2 + 7 x - 9 with respect to x is:
f'(x) = 12 x3 - 10 x2 + 7
f'(x) = 12 x2 - 10 x
f'(x) = 12 x2 - 10 x + 7
f'(x) = 4 x2 - 5 x + 7
2.
The slope of the tangent line to the curve y = x2 - 6 x + 5 at the point (4, -3) equals:
m = -3
m = 8
m = -2
m = 2
3.
If y = (2x + 1) * (3x - 4), then dy/dx evaluated at x = 1 equals:
12
1
7
-5
4.
Using the Quotient Rule, the derivative of y = (x + 3) / (x - 2) for x != 2 is:
-5 / (x - 2)2
1 / (x - 2)2
5 / (x - 2)2
(2x + 1) / (x - 2)2
5.
According to the Chain Rule, if y = (3 x2 - 5)4, then dy/dx is:
6 x (3 x2 - 5)3
12 x (3 x2 - 5)4
24 x (3 x2 - 5)3
4 (3 x2 - 5)3
6.
The derivative of y = sin(3x) with respect to x is:
cos(3x)
-3 cos(3x)
3 cos(3x)
3 sin(3x)
7.
If a particle moves along a straight line such that its position s(t) = t3 - 6 t2 + 9 t meters, the particle comes to an instantaneous rest (velocity v(t) = 0) at times:
t = 1 second and t = 3 seconds
t = 6 seconds
t = 0 seconds only
t = 2 seconds and t = 4 seconds
8.
The equation of the tangent line to the curve y = x3 at the point (1, 1) is:
y = 3x + 1
y = x
y = 3x - 2
y = -3x + 4
9.
The second derivative d2y/dx2 of the function y = x4 - 2 x3 + 5 is:
4 x3 - 6 x2
24 x - 12
12 x2 - 6 x
12 x2 - 12 x
10.
If f(x) = |x - 3|, the derivative f'(3) at x = 3:
Equals 0
Equals 1
Equals -1
Does not exist because the left-hand derivative (-1) does not equal the right-hand derivative (+1)
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