Calculus Year in Review

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 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)

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

• infinity

• negative infinity

• 0

• 1

• Does not exist
• 6
• 4
• 3

• 0
• 2
• 3
• 4

The slope of a function is described by its ____________.

• first derivative
• second derivative
• third derivative
• expression

If a function's FIRST derivative is negative at a certain point, what does that tell you?

• The function is increasing at that point
• The function is decreasing at that point
• The concavity of the function is up at that point
• The concavity of the function is down at that point