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Return to Foundations of Science Mathematics 2e Student Resources
Chapter 4 Multiple choice questions
Differentiation
Quiz Content
*
not completed
.
Which of the following is
not
true about the derivative, d
y
/d
x
, of a function,
y
= f(
x
) ?
The function must be continuous for it to exist.
correct
incorrect
The function must be smooth for it to exist.
correct
incorrect
It gives the slope, or gradient, of the function.
correct
incorrect
It is equal to the sine of the angle of the slope.
correct
incorrect
*
not completed
.
If
y
= e
^{-}
^{x}
cos(
x
^{2}
), what is d
y
/d
x
?
[ – cos(
x
^{2}
) – 2
x
sin(
x
^{2}
) ] e
^{-}
^{x}
correct
incorrect
[ – cos(
x
^{2}
) + 2
x
sin(
x
^{2}
) ] e
^{-}
^{x}
correct
incorrect
[ cos(
x
^{2}
) – sin(
x
^{2}
) ] e
^{-}
^{x}
correct
incorrect
[ cos(
x
^{2}
) + sin(
x
^{2}
) ] e
^{-}
^{x}
correct
incorrect
*
not completed
.
If
y
=
x
ln(
x
) + exp(-
x
^{2}
), what is d
y
/d
x
?
ln(
x
) + exp(-
x
^{2}
)
correct
incorrect
ln(
x
) – 2
x
exp(-
x
^{2}
)
correct
incorrect
1 + ln(
x
) – 2
x
exp(-
x
^{2}
)
correct
incorrect
1 + ln(
x
) + exp(-
x
^{2}
)
correct
incorrect
*
not completed
.
What is the lowest value of
y
for the function
y
=
x
^{2}
[ 3
x
^{2}
– 4
x
– 12] ?
0
correct
incorrect
-5
correct
incorrect
-32
correct
incorrect
Unbounded, tends to minus infinity.
correct
incorrect
*
not completed
.
What is the nature of the stationary point that has d
^{2}
y
/d
x
^{2}
= 0 ?
It is a maximum.
correct
incorrect
It is a minimum.
correct
incorrect
It is a point of inflexion.
correct
incorrect
Any of the above is possible.
correct
incorrect
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