Derivatives
The derivative of y = 3x2 - 4
What is dy/dx = 6x
The slope of the tangent line of y = 5x2 - 4x at x = 1.
What is 6
The slope of the curve is found using
What is the first derivative?
A numberline with f'(x) finds intervals of
Increasing and decreasing.
This historical genius is known to have discovered Calculus and served as a chair at Cambridge University
Who is Isaac Newton?
The first derivative of f(x) = -6x2 + 10x - 14.
What is f'(x) = -12x + 10
The equation of the tangent line to y = 2x3 - 6 at x=2 using the formula y-y1=m(x-x1) where (x1,y1) is a point and m is the slope
What is y - 10 = 24(x-2)
The process of finding critical points.
Setting first derivative equal to zero or undefined.
A critical point where f'(x) changes from negative to positive.
What is a local maximum?
This man is known for shouting "Eureka!" when he discovered he could measure volume by water displacement.
Who is Euler?
The first derivative of y = sqrt(x)
What is y' = 1/ (2sqrt(x) )
The x-coordinate of the critical points of the function f(x) = x2+x-6.
What is x = -1/2
The condition for a function f(x) to be increasing.
What is f'(x) > 0
The condition for a function to be concave up.
What is f''(x) > 0?
The biggest controversy over who invented calculus is between these two people.
Who are Isaac Newton and Godfried Leibniz?
The second derivative of
y = 6x^4 - 1/2 x^2 - 10
What is
y' = 72x^2 - 1
Classify the critical point on y = 1/3x3 + 1/2x2 - 6x at x=2
What is a local minimum
The condition for a function f(x) to be concave down.
What is f''(x) < 0?
A point on a curve where the tangent line is horizontal and the curve is concave down.
What is a local maximum?
This man, whose name translates to "hospital" is known for coming up with a calculus rule named after him.
Who is L'Hôpital?
Find the derivative of
(10x^2-7x)/(3x^4-5x^6)
f'(x) =
((20x-7)(3x^4-5x^6))/((12x^3-30x^5)(10x^2-7x))
The x-coordinate of the inflection point on the curve y = 1/6x3 + 3/2 x2.
What is x = -3?
The conditions for a point of inflection to occur.
What is f''(x) = 0 or undefined with a change in concavity?
The use of the second derivative test
What is classifying points where the tangent line to the curve is horizontal?
This function maintains its identity when you take its derivative.
What is ex?