12th AP Cal product and quotient rule

Given f (x) = 5sinx + 3x³cosx, f '(x) =

• -5cosx − 3x³sinx + 9x²cosx
• 5sinx − 3x³sinx + 9x²cosx
• 5cosx − 3x³sinx + 9x²cosx
• 5cosx + 3x³sinx + 9x²cosx

Find the derivative of g(x)=(3x-2)/(x²+2)

• 3/(2x)
• (-3x²-4x +6)/(x²+2)²
• (-3x²+4x +6)/(x²+2)²
• (-3x²+10)/(x²+2)²

How do you find horizontal tangent lines?

• Find where the derivative is undefined
• Find where the derivative equals zero
• Find where the derivative is 1
• Find where the derivative is negative

Derivative means the same thing as

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

Given that the position function for a particular object is given by 
s(t) = t³ - 3t +5, find the acceleration of the object at t = 2 seconds. 

• 27
• 12
• 6
• -2

Use the product rule to determine the derivative.

• 4x⁸+60x⁶+12x³

• 12x⁷+36x²

• 32x⁷+36x²

• 20x⁶

Find an equation of the tangent line to the graph of f(x) at the point (1, 100)
f(x) = (5x⁵ + 5)²

• y = 500x + 400
• y = 100x + 400
• y = -500 x - 400
• y = 500x - 400

Find the slope of the tangent line to f(x) = -3x²-6x at x = 1.

• m = 0
• f'(x) = -6x - 6
• f'(x) = 6x
• m = -12

If the position function for a particle is s(t) = -t² - t, what is the instantaneous velocity function for the particle? 

• v(t) = -2
• v(t) -2t - 1 
• v(t) = t³
• v(t) = -t

• cscx cotx
• secx tanx
• sec²x
• -cscx cotx

Tags

CCSS.HSF.TF.C.8