Unit 3 Review Miscellaneous

Derivative means the same thing as

• slope of the tangent line
• slope of the normal line
• exponent
• slope of the secant line

At which point(s) will the slope(s) of the tangent line be POSITIVE?

• at C only

• at points A, C and E only

• at point B and D only

• at points A and E only

Find the derivative f(x) = tanxcosx

• f'(x) = sec²xcosx - tanxsinx
• f'(x) = sec²xcosx + tanxsinx
• f'(x) = sec²xsinx
• f'(x) = sec²xcosx - tanxcosx

What is the derivative of y = 2π?

• 0

• 2

• -2

• None of the above

Set up the derivative of

y=(3x⁴ - 7)(5x² + 1)

• y' = (12x³)(10x)

• y' = (3x⁴ - 7)(10x) + (12x³)(5x² + 1)

• y' = (3x⁴ - 7)(10x) - (12x³)(5x² + 1)

• y' = (3x⁴ - 7)/(10x) + (12x³)/(5x² + 1)

Find the derivative of y = x⁴⋅cos x

• y' = x⁴ cosx - 4x³sinx

• y' = 4x³ cosx - x⁴sinx

• y' = 4x³ cosx + x⁴sinx

• y' = -4x³cosx

True or False: It is possible for a function to be continuous, but not differentiable.

• True

• False

• What do you mean?

True or False: It is possible for a function to be differentiable, but not continuous.

• True

• False

• Nope, I've had enough of this.

A function f(x) has a tangent line at x = 3, which is y = 4x - 1.

Based on this alone, the function f(x) must be continuous at x = 3.

• True

• False

• Calculus

At a point where a function has a corner, what describes the function's continuity and differentiability?

• It is both continuous and differentiable.

• It is continuous, but not differentiable.

• It is differentiable, but not continuous.

• It is neither continuous nor differentiable.