Stationary point
The equation of a curve is such that d^2y/dx^2=3x^2-6 . The point P (2,3) is a stationary point on the curve. By evaluating second derivative at P, determine the nature of this stationary point.
Minimum
The equation of a curve is such that dy/dx=kx^3+2/x^2, where k is a constant. The curve passes through the point S (2, 20) and the gradient of the curve at S is 65/2 . Find the value of k
k=4
What city does Batman protect?
Gotham City
Which song is the most streamed one on Spotify? (Bonus 300 points if your team sings it)
"Blinding Lights" – The Weeknd (~5.6B+ streams)
What is the biggest planet in our solar system?
Jupiter
y=5x^4-24x^3+42x^2-32x+11 Find the stationary point
A curve has equation y = 0.5(4x-3)^-1. The point A on the curve has coordinates (1,0.5). Find and simplify the equation of the normal through A.
y=0.5x
What is Captain America’s shield mainly made of?
Vibranium
What was the first video to reach one billion views on YouTube?
"Gangnam Style" by PSY
How many reindeer does Santa Claus have? (Bonus 600 points if you can name them all)
9
Dasher, Dancer, Prancer, Vixen, Comet, Cupid, Donner, Blitzen, and Rudolph
The function f is defined by f(x)=16/x^3+3x+5 for x is not equal to 0. (a) Find the coordinates of all stationary points on the curve y= f(x).
A curve passes through the point P (4, 3) and is such that dy/dx=8/x^2-10/(2x-3)^2 Find the equation of the normal to the curve at P. Give your answer in the form y=mx+c
y=-10x+43
The baby from The Incredibles name
Jack-Jack
Which artist released the album "1989"?
Taylor Swift
What year was TikTok introduced?
2016
A curve has equation y=k(3x-k)^-1+3x, where k is a constant. Find, in terms of k, the values of x at which there is a stationary point.
x=(k+-√k)/3
y=3√(4x+1)-2x Obtain expressions for first derivative and integration of the equation.
picture
In Ratatouille, what is the name of the restaurant Remy dreams of cooking in?
Gusteau's
Which artist has won the most Grammy Awards of all time?
Beyoncé
Name two countries' flags with pink in them?
Mexico and Spain
The curve C has equation y=9x-x^3 Sketch C showing the coordinates of the points at which the curve cuts the x-axis.
the graph
The equation of the curve is such that d^2y/dx^2=6x^2-4/x^3. The curve has a stationary point at (-1,9/2). Determine the nature of the stationary point and find the equation of the curve.
picture
Which kdrama is the best rated on IMDb?
When Life Gives You Tangerines (2025) 9.0/10
Who performed the Super Bowl halftime show in 2023?
Rihanna
Which civilization built Machu Picchu?
The Inca civilization