Calculus - Ch 5 Review

Rachel is standing atop a 13 ft ladder. The ladder is leaning against a vertical wall. The ladder starts sliding away from the wall at a rate of 3 ft/sec. How fast is the ladder sliding down the wall when the tip of the ladder is 5 ft high?

• 3 ft/sec
• -7.2 ft/sec
• 7.2 ft/sec
• 12

Rachel is standing atop a 13ft ladder. The ladder is leaning against a vertical wall. The ladder starts sliding away from the wall at a rate of 3ft/sec.  How fast is the angle changing between the base of the ladder and the ground when the ladder is 5 ft high?

• -1.44 deg/sec
• 1.5 deg/sec
• .5 deg/sec
• .65 deg/sec

Chris is sitting on the edge of a dock tossing rocks into the water. As each rock hits the water, small circles appear traveling outward from the point of impact. The radius of the circle is changing at a rate of 5 in/sec.  How fast is the area changing when the circumference is 4 in? 

• 40 in/sec
• 20 in/sec
• 20pi in/sec
• 40pi in/sec

A water tank, shaped like an inverted circular cone, has a base radius of 6 ft and a height of 9 ft. The tank is completely full and needs to be drained. The valve is opened and the water begins to decrease at a rate of 2 ft³/sec.  How fast is the height of the water changing when the water is 2 ft deep?

• -9/(8pi) ft/sec
• 9/(8pi) ft/sec
• -8/(9pi) ft/sec
• 8/(9pi) f/tsec

A closed rectangular shipping box with square base is to be made from 120 square inches of cardboard. What dimensions should the box be for maximum volume?

Choose the constraint and optimization equations that represent the problem. 

•  $x^2=120$  and  $V=x^3$  

•  $2x+y=120$  and   $V=xy$  

•  $x^2y=120$  and  $V=2x^2+4xy$  

•  $2x^2+4xy=120$  and  $V=x^2y$  

A rectangle is bounded by the x-axis and the parabola  $y=12-x^2$ .  What length and width should the rectangle have so that its area is a maximum?  

Given the constraint equation above and the optimization equation  $A=2xy$  , choose the DERIVATIVE of the merged (combined) equation.

•  $A'=2xy$  

•  $A'=\ \ 24-6x^2$  

•  $A'=2x\left(12-x^2\right)$  

•  $A'=12-2x$  

What is the linearization function L(x) for
y = (2x-1)² for values of x near 3?

• L(x) = 20x - 35
• L(x) = (2x - 1)² (x - 3)
• L(x) = -4x + 1
• L(x) = 4(2x - 1)

Find dy for the function y = 4x² + x + 3.

• (8x² + x + 3)dx
• (4x + 1)dx
• (8x + 1)dx
• 8x + 1

Tags

CCSS.HSF.LE.B.5

Find dy for 2xy² - x² + y = 5 if x = 0 and dx = 0.01. 

• -50
• -0.5
• -5
• (2x - 2y²) / (4xy + 1) dx

Use the linear approximation of  $y=\sqrt{x}$  at x = 25 to estimate the value of $\sqrt{23}$ to the nearest tenth.

• 4.6

• 4.7

• 4.8

• 4.9