Intro to Calc - Practice Opener #4

• A
• B
• C
• D

• A
• B
• C
• D

The value of the definite integral for the shaded region on the parabola y = x² - 5x is:

• -39.33

• 20.833

• 106.67

• -20.833

• 39.33

If f(x) = sin³(2x), then f'(x) =

• 3cos(2x)
• 3sin(2x)⋅2
• 3sin²(2x)cos(2x)
• 3sin²(2x)cos(2x)⋅2

Tags

CCSS.HSF.TF.C.9

• -csc(2x)cot(2x)
• -4csc(2x)cot(2x)
• -csc²(2x)
• 4sec(2x)

If f(x) = sec(4x), then f'(x) =

• 4sec(4x)tan(4x)
• 2sec(4x)tan(4x)
• -4csc(4x)cot(4x)
• -2csc(4x)cot(4x)

When we "take the derivative" of a function what are we finding?

• What's a derivative?
• The rate at which our struggles in Calculus are increasing.
• The slope of the secant line
• The slope of the tangent line

Product Rule in relation to derivatives. 

• uv' - vu'
• uv' + vu'
• v'u'
• uv

d/dx (sin³(4x^-6)) = ?

• -24x^-5 ⋅ cos (4x^-6) ⋅ 3sin²(4x^-6)
• -24x^-7 ⋅ cos (4x^-6) ⋅ 3sin²(4x^-6)
• -24x^-7 ⋅ 3cos²(4x^-6)
• 3cos²(-24x^-5)

Find the derivative.

• x⁴ cosx - 4x³sinx
• x⁴ cosx + 4x³sinx
• 4x³cosx
• -4x³cosx