Derivative of the outer, with respect to the inner, times the derivative of the inner. Thats the chain rule!
Must sing for full credit.
100
On the curve of y= x^2, is LRAM an under or over approximation? Why?
Underapproximation. Boxes are inside of the parabola.
100
Favorite kind of oatmeal?
Yellow Curry
200
What does the derivative of a function of a certain point tell us?
Slope of the tangent line.
200
Mean value theorum for a definite interval?
If f is continuous on [a,b], then at some point, c, in [a,b], f(c) = [F(b)- F(a)]/ (b-a)
200
What is part 1 of the Fundamental Theorum of Calculus?
If f is continuous on [a,b], then the function =
integral a --> b f(t)dt has a derivative of every point x in [a,b] and dF/dx = d/dx int a --> x f(t)/dt = f(x)
200
What formula do you use when writing the equation of a tangent line?
Point Slope
200
How many children does Mrs. Lalwani have?
2
300
Suppose that r(x)= 9x and c(x)= (x^3) - 6(x^2) - 15x, where x represents thousands of units. Is there a production level that maximizes profit? If so, what is it?
Maximum profit occurs at approx: x= 3.414
300
y = sec^2x , interval = (0, pi/4), find the average value of the function.
4/pi
300
Newton's Law of Cooling, give the formula.
T-Ts = (T0-Ts) * e^(-kt)
T0 = time when time (t)= 0
Ts = temp of surroundings
300
If you have the slope of the tangent line, how do you find the slope of the normal line?
Find the negative reciprocal of the slope of the tangent line
300
What is her drink of choice in the morning?
Coffee
400
A hot air balloon rising straight up from a level field is tracked by a range finder 500 ft. from the lift off point. At the moment the range finder's elevation angle is pi/4. The angle is increasing at a rate of 0.14 radians per minute. How fast is the balloon rising at that moment?
Rate = 140 ft. per minute
400
DAILY DOUBLE: What is Mrs. Lalwani's favorite movie?
The Italian Job
400
What is the derivative of tanx?
(sec(x))^2
400
A hard boiled egg at 98 degrees C, is put in a pan under running, 18 degree C water to cool. After 5 minutes, the eggs temperature is found to be 38 degrees C. How much longer will in take the egg to reach 20 degrees C?
In just over 8 additional minutes, 13.3 minutes total
400
True or False: Calculus is easy (according to Mrs. Lalwani)
True......
500
A spherical balloon is inflated at a rate of 100pi ft. cubed per minute.
a) How fast is the balloons rate increasing at the instant the radius is 5ft?
b) How fast is the surface area increasing at that minute?
a) 1 ft. per minute
b) 40pi ft. squared per minute
500
Find the integral from (-1,1) of 1/(1+x^2) dx.
pi/2
500
What is product rule?
f(x)*g(x) = f(x) * g'(x) + f'(x) * g(x)
500
DOUBLE JEOPARDY: Is math fun?
Only higher level.
500
Name at least one University Mrs. Lalwani received a degree from.