Derivatives
Derivative of f(x) = x2
What is 2x?
∫xdx
What is 1/2x2 + c?
The area under the curve from a to b represents
What is the definite integral of the function from a to b?
The symbol ∫ represents
What is an integral?
Derivative of f(x) = 3x3 + 2x
What is 9x2 + 2?
∫3x2dx
What is x3 + c?
True or false: the area under the curve can be negative (explain)
What is true OR false (depending on explanation): if the curve is below the x-axis, the definite integral is negative, however, the area itself cannot be negative, hence why absolute value is often used
Co-founder of calculus alongside Isaac Newton
What is Gottfried Leibniz?
Derivative of f(x) = sin(x)
What is cos(x)?
∫cos(x)dx
What is sin(x) + c?
Area under the curve of f(x) = x from x = 0 to x = 2
What is 0∫2 xdx?
What is The Fundamental Theorem of Calculus?
Derivative of f(x) = 1/x
What is -1/x2?
∫(1/x)dx
What is ln(x) + c?
Area under the curve of f(x) = 2x from x = 0 to x = 3
What is 0∫3 2xdx?
True or false: a function must be continuous to have a derivative at a point
True: differentiation requires continuity
Derivative of f(x) = x2 * ln(x)
What is 2xln(x) + x?
∫e2xdx
What is (1/2)e2x + c?
Find the area between the x-axis and f(x) = x2 from x = 0 to x = 3
What is let's solve (you can join, Mr. Liss)!
The only planet in our solar system to rotate clockwise on its axis
What is Venus?