Calculus Derivatives Quiz

The operation of finding the derivative of a function is called?

• Differentiability

• Continuity

• Differentiation

• Differentiability and Continuity

If a function f(x) is differentiable at x = a, then function f(x) is continuous at?

• x = a

• x = x

• a = x

• f(x)

Which of the following statement/s is/ are true? I. A function that is continuous at x=a is differentiable at x=a II. A function that is differentiable at x=a is continuous at x=a III. A function that is NOT continuous at x=a is NOT differentiable at x=a IV. A function that is NOT differentiable at x=a is NOT continuous at x=a

• I and III

• I and IV

• II and IV

• I, II, III, IV

Find the derivative of 6x4-7x3+5x2.

• 2x4-12x3+10x

• 24x3-21x2+10x

• 26x4-7x3+5x2

• 6x4-27x3+5x2

Find the derivative of ddx(log4x2).

• 1x ln 4

• 2x ln 2

• 2x ln 4

• 22x ln 4

Find the derivative of ddx=[4tanx].

• 4tanxsec2x ln4

• 2tanxsec2x ln4

• 4tanxsec2x ln

• 2tanxsec2x ln

Which among the statements is true?

• The derivative of a constant is 1.

• The derivative of a constant is -1.

• The derivative of a constant is 0.

• The derivative of a constant is x or y.

Find the derivative of ddx(log5x2).

• 2x ln 5

• 1x ln 2

• 1x ln 5

• 22x ln 5

Which among the equations is true?

• f(x)=1, then f'x=1

• f(x)=1, then f'x=0

• f(x)=1, then f'x=1+x

• f(x)=1, then f'x=1+2x

Which of the values is the absolute maximum of the function f(x) = 4x - x2 + 6 on the interval [0, 4]?

• 0

• 2

• 4

• 10