AP Calculus Review Assessment

What is the derivative of y= 1 - x² + x - 3x⁴

• y^/=x+-2x+1-12x³

• y^/=x-x³/3+x²/2-3x⁵/5

• y^/=-2x+1-12x³

• y^/=2x+1-12x³

what is the derivative of y= sin(2x)?

• y^/=cos(2x)

• y^/=2sin(2x)

• y^/=2sin(x)+cos(2x)

• y^/=2cos(2x)

when is the function f(x)=x²+6x+9 increasing?

• (3,∞)

• (-∞,3)

• (-3,-∞)

• (-3,∞)

What is the speed of the position function f(x)=-3x²-6x-6 at x=2

• -18

• 18

• -6

• 6

What is the integral of f(x)=sin(2x)+1/x

• -2cos(2x)+ln(x)+c

• ln(|x|)−cos(2x)/2+C

• ln(|x|)−cos(2x)/2

• ln(|x|)+cos(2x)/2+C

Let f be the function defined by f(x)=4x³-10x+5. Find the equation of the tangent line to the graph of f at the point where x = 1

• y+1=2(x-1)

• y-1=2(x-1)

• y+1=2(x+1)

• y+1=-2(x-1)

If g is the inverse function of F and f(2)=3, find the value of g'(3) for F(x)=6x²+2x-1

• 1/24

• 1/25

• 1/26

• 26

what is the limit as x approaches infinity of the function f(x)= (3x-5)/(5x²+4)

• infinity

• negative infinity

• 0

• 1

what is the average rate of change of the function f(x)=x²-6x+6 from 2 to 6?

• 4

• 2

• 3

• 23/4

What are the conditions that satisfy the mean value theorem, and what does it mean?

• Continuous on the open and differentiable on the closed, and then there is at least 2 numbers c and d in the interval (a,b) (that is a < c < b) such that

• Discontinuous on the closed and differentiable on the open, then there is at least one number c in the interval (a,b) (that is a < c < b) such that f'(c)=(f(b)- f(a))/ (b-a)

• Continuous on the closed and differentiable on the open,and then there is at least one number c in the interval (a,b) (that is a < c < b) such that f'(c)=(f(b)- f(a))/ (b-a)

• Continuous on the open and differentiable on the open, and then there is no number c in the interval (a,b) (that is a < c < b) such that f'(c)=(f(b)- f(a))/ (b-a)