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Differentiation - Quiz 1   Last unanswered question  Question  Next unanswered question

Question 1 lion

Which of the following is the derivative of y = x2 + 7 ?
a) dy-= 2x+ 7.
dx    b) dy-= 2x.
dx
c) dy
--= 2x2 .
dx    d)  dy   1 3
dx-=  3x + c.

 

Not correct. Choice (a) is false.
Try again, the derivative of a constant is zero.
Your answer is correct.
d-(xn) = nxn-1
dx  so  d
---(x2 + 7) = 2x+ 0 = 2x.
dx
Not correct. Choice (c) is false.
Try again, remember d
--(xn) = nxn- 1.
dx
Not correct. Choice (d) is false.
Try again, remember  d  n      n-1                       2
dx-(x  ) = nx  , you have integrated y = x .
Question 2 lion

Which of the following is the derivative of       3 V~ --
f(x) =  x ?  Recall  V~ n-   1n
  x = x .
a)  '     3 V~  -
f (x) =   1.    b)        3 V~ 3-
f'(x) = -  x4.
       4
c)   '    2 3 V~ -2
f (x) = 3 x  .    d) f'(x) = -1 V~ ---.
       3 3x2

 

Not correct. Choice (a) is false.
Try again, convert        V~ 3-   13
f(x) =  x = x   and then use the differentiation rules.
Not correct. Choice (b) is false.
Try again, you have integrated  V~ 3-
  x.
Not correct. Choice (c) is false.
Try again, convert       3 V~  --   1
f(x) =  x = x 3   and then use the differentiation rules.
Your answer is correct.
f(x) =  V~ 3x-= x 13   and f'(x) = 1x -23 =-1--= - V~ 1-.
       3       3x23   3 3 x2
Question 3 lion

Which of the following is the derivative of y = 1-?
    x2
a) dy= - -2 .
dx    x3    b) dy= - 2-.
dx    x
c) dy   2
--=  -3 .
dx   x    d)  dy   1
dx-=  2x .

 

Your answer is correct.
y =-1 = x-2
   x2  and dy-= -2x -3 = - 2-.
dx             x3
Not correct. Choice (b) is false.
Try again, convert y =-1 = x-2
   x2  and then use the differentiation rules.
Not correct. Choice (c) is false.
Try again, look carefully at the sign.
Not correct. Choice (d) is false.
Try again, convert     1
y = x2 = x-2  and then use the differentiation rules.
Question 4 lion

Which of the following is the second derivative of f(x) = 4x3- 11x2- 14x+ 19 ?
a) f''(x) = 12x2 - 22x- 14.    b) f''(x) = 12x - 22.
c) f''(x) = 24x- 22.    d) f ''(x) = 4x- 11.

 

Not correct. Choice (a) is false.
Try again, this is the first derivative.
Not correct. Choice (b) is false.
Try again, note that f'(x) = 12x2- 22x- 14 .
Your answer is correct.
f'(x) = 12x2- 22x - 14 , so f''(x) = 24x- 22.
Not correct. Choice (d) is false.
Try again, you must differentiate each term twice.
Question 5 lion

The gradient of the curve     2
y = x -5x + 6  is zero at which of the following values of x ?
a) x = 2  and x = 3 .    b) x = 2.5 .
c) x = 6.    d) -dy= 2x - 5.
dx

 

Not correct. Choice (a) is false.
Try again, this is where the function is zero, not where the gradient is zero.
Your answer is correct.
dy-
dx = 2x- 5,  so dy-
dx = 0  when 2x - 5 = 0 ==> x = 5 = 2.5.
                2
Not correct. Choice (c) is false.
Try again, 6 is the y  -intercept.
Not correct. Choice (d) is false.
Try again, this is the gradient function but doesn’t answer the question.