A function which gives the slope of a curve; that is, the slope of the line tangent to a function.
when f double prime changes sign
Describes the motion of an object. The derivative of a velocity function v(t) or the double derivative of a position function s(t).
f a real-valued function f is continuous in the closed and bounded interval [a,b], then f must attain a maximum and a minimum, each at least once.
if a continuous function, f, with an interval, [a, b], as its domain, takes values f(a) and f(b) at each end of the interval, then it also takes any value between f(a) and f(b) at some point within the interval
Describes the motion of an object. The derivative of a position function s(t)
Down
the process of finding the derivative of a dependent variable in an implicit function by differentiating each term separately, by expressing the derivative of the dependent variable as a symbol, and by solving the resulting expression for the symbol
d/dx (fg)=f'g+g'f
f(x) has to be continuous and differentiable
defined over [a, b] (for closed--all numbers from a-b including a and b--versus open (a, b) which means all numbers from a-b not including a and b)
if this is true, f'(c)=f(b)-f(a)/(b-a)
d/dx (x^n)=nx^(n-1)
d/dx (f/g)=(f'g-g'f)/g^2
derivative of the function is zero or does not exist
Given as a function of x with respect to time, x(t). An object's change in position with respect to time is known as its displacement.
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