Derivatives Review

What is an equation of the tangent line to the graph of f(x)=xsinx-2x+7 at the point (0,7)?

• y= -2x-7

• y= -2x+7

• y=7x-2

• y=7x+2

Tags

CCSS.HSF.IF.A.2

Which graph shows a function whose derivative is always negative?

• A

• B

• C

• D

Hint: You do not need the quotient rule.

• 6-6x

• 6

• 6x

• -6

If h(x)=|2x-5|, which of the following is true?

• h is continuous but is not differentiable at x=5/2

• h is not continuous but is differentiable at x=5/2

• h is continuous and differentiable at x=5/2

• h is neither continuous nor differentiable at x=5/2

If f(x)=sinx/x², then f'(x)=

• cosx/2x

• (xcosx-2sinx)/x²

• (xcosx-2sinx)/x³

• (cosx-2sinx)/x²

If y=∜(8x+3), then y'=

• 2/(8x+3)^3/4

• 1/(4(8x+3)^3/4)

• (1/4)(8x+3)^3/4

• 8/(8x+3)^3/4

Find the derivative of the function f(x)=x⁸√(5-3x)

• x⁷(80-3x)/(2√(5-3x))

• x⁷(80+51x)/(2√(5-3x))

• x⁷(5+3x)/(2√(5-3x))

• x⁷(80-51x)/(2√(5-3x))

Find the derivative of the function g(x)=((x+6)/(x²+7))⁴

• 4(7-12x-x²)(6+x)³/(7+x²)⁵

• 4(7+12x-x²)(6+x)³/(7+x²)⁵

• 4(7-12x-x²)(6+x)⁵/(7+x²)³

If y=sinx, then y⁽⁴⁾=

• sinx

• cosx

• -sinx

• -cosx

Tags

CCSS.HSF.TF.C.9

If y=6cos(2x), then y⁽⁶⁾=

• 384cos(2x)

• -384cos(2x)

• 384sin(2x)

• -384sin(2x)