Derivatives
The derivative of 6x3â9x+4
What is fâ˛(x)=18x2â9
The anti-derivative of 8x3 d(x)
What is 2x4 + C
This theorem requires the function to be both continuous and differentiable.
What is the mean value theorem?
A function is continuous at c if
What is when f(c) is defined, when the limit as f(x) approaches c exists, and when f(c)=the limit as f(x) approaches c.
The limit as x approaches 3 for f(x)=(8-3x+12x2)
What is 50?
The derivative of (2x2)(x3+1)
What is (2x2)(3x2)+(4x)(x3+1)
The anti-derivative of sin(2x)d(x)
What is -1/2cos(2x)+C
When a function is continuous and f(-2)=3 and f(1)=6, the intermediate value theorem guarantees this:
What is f(c)=4 for at least one c between -2 and 1?
A particle is moving on a line, the velocity of this particle is a positive value. This means the particle is moving to the
What is to the right?
The derivative of 3x+2/x2
What is x2(3)-(3x+2)(2x)/(x2)2
The anti-derivative of ln(5x)
What is 1/5x+C
The extreme value theorem can guarantee what on a continuous function
What is a maximum and a minimum value?
At a value c, the derivative of f(x) crosses over the x-axis, the values go from negative to positive. On the graph of f(x) the value c is a
What is a minimum?
The derivative of sin2(12x3)
What is 2sin(12x3) (cos(12x3)) (36x2)
The anti derivative of (3x+6)/(x2+4x-3)
What is (3/2)ln|x2+4x-3|+C
Someone would use this to solve for the derivative of F(x) when F(x)= the anti derivative of f(t) from a value 'a' to 'x'.
A left reimann sum is an ____estimate if the curve is decreasing.
What is an overestimate?
The limit as x approaches -5 when f(x)= (x2-25)/(x2+2x-15)
What is 5/4?
The derivative of 6e4x
What is 24e4x
The anti derivative of 3/(xln(x))
What is 3ln|lnx|+C
This theorem goes along with MVT
What is Rolle's Theorem?