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 simplified first derivative of g(x)=(x2-4x)(x3+1)
What is g'(x) = 5x4-16x3+2x-4
The first derivative of f(x)=(x2+1)1/2
What is f'(x)=x/(x2+1)1/2
Setting first derivative equal to zero.
The process of finding critical points.
A stationary point where f'(x) changes from negative to positive.
What is a local maximum?
The first derivative of y = sqrt(x)
What is y' = 1/ (2sqrt(x) )
The equation of the tangent line to y = 2x3 - 6
What is y - 10 = 24(x-2)
The simplified first derivative of f(x)=(6x2+x-8)(x2+x-2)
What is f'(x)= 4x3+6x2-18x-10
The slope of the tangent to f(x)=5/(2x-x2)1/3 at x=1
what is 0
A numberline with f'(x) finds intervals of
Increasing and decreasing.
The condition for a function to be concave up.
What is f''(x) > 0?
The second derivative of y = 6x4 - 1/2 x2 - 10
What is y' = 72x2 - 1
The coordinates of the points on the graph of f(x)=x3-7x where the slope of the tangent is 5
What is (2,-6) and (-2, 6)
The first derivative of h(x)=(x2-1)/(x3-8)
what is h'(x) = (x4-3x2+16x)/(x3-8)2
The equation of the tangent to y=(x3-4x2)3 at x=3
What is y=729x-2196
The condition for a function f(x) to be concave down.
What is f''(x) < 0?
A stationary point that is concave down.
What is a local maximum?
The second derivative of y=3/(x1/3)
What is y=4/(3x7/3)
The values of a and b for f(x)=ax3+bx2+3x-2 given that f(2)=10 and f'(-1)=14
what is 2 and -5/2
The second derivative of f(x)=(x2+1)1/2
What is f''(x)=1/(x2+1)(3/2)
This function is the derivative of (sin(x))^3.
What is 3( sin(x) )^2 cos(x) ?
The conditions for a point of inflection to occur.
What is f''(x) = 0 and a change in concavity.
The use of the second derivative test
DETERMINING MAX AND MINS