Unit 3 part II differentiation + 4.1-4.3 particle motion

What is the derivative of a function?

• The derivative is the area under the curve of the function.

• The derivative of a function at a point is the slope of the tangent line to the graph of the function at that point.

• The derivative measures the total distance traveled by the function.

• The derivative is the maximum value of the function.

What is the relationship between the derivative and the slope of a curve?

• The derivative at a point gives the slope of the tangent line to the curve at that point, indicating how steep the curve is at that location.

• The derivative measures the area under the curve at a given point.

• The derivative is the average slope of the curve over an interval.

• The derivative indicates the maximum height of the curve at a specific point.

What is the slope of the tangent line?

• The slope of the tangent line is the second derivative of the function.

• The slope of the tangent line is given by the integral of the function.

• The slope of the tangent line at a point on a curve is given by the derivative of the function at that point.

• The slope of the tangent line is the average rate of change of the function over an interval.

Find dy/dx by Implicit Differentiation 
x³ +y³  = 36

• 6 -x
• 3x² +3y² 
• −x²/y²
• 0

Find   $\frac{dy}{dx}$  :  $2x^2-3y^2=4$  

•  $\frac{2x}{y}$  

•  $\frac{x}{3y}$  

•  $\frac{3y}{2x}$  

•  $\frac{2x}{3y}$  

Find the derivative at a point.

• 2/3

• -2/3

• 1

• -1

Find the derivative of  $x^2+xy+y^3=0$  

•  $-\ \frac{2x}{1+3y^2}$  

•  $-\frac{x+3y^2}{2x+y}$  

•  $-\frac{2x+y}{x+3y^2}$  

•  $-\frac{2x}{x+3y^2}$  

find y' for y= sin(2x²)

• 4sin(2x²)

• 4xcos(2x²)

• 2xcos(2x²)

• xcos(4x²)

Find dy/dx if y = sec(8x²).

• sec(16x)tan(16x)
• 16xcos(8x²)
• 16xsecxtanx(8x²)
• 16xsec(8x²)tan(8x²)

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