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Calculus Project

the speed of something in a given direction.
If f and g are both differentiable, then d/dx[f(x)g(x)] = f(x)(d/dx)[g(x)] + g(x)(d/dx)[f(x)]
If f’ changes from positive to negative at x=c, f has a relative max at x=c. If f’ changes from negative to positive at x=c, f has a relative min at x=c
Each of four parts of a plane, sphere, space, or body divided by two lines or planes at right angles.
Suppose that f is continuous on the closed interval [a,b] and let N be any number between f(a) and f(b), where f(a) does not equal f(b). Then there exists a number c in (a,b) such that f(c)= N.
The value that a function or expression approaches as the domain variable(s) approach a specific value.
The rate of change on which a function follows in an interval.
any point at which the value of a function is largest (a maximum) or smallest (a minimum).
the action of making the best or most effective use of a situation or resource.
if F is a continuous function on the closed interval [a,b], then F must attain a maximum and a minimum, each at least once, on [a,b].
If n is a positive integer, then d/dx (x^n) = nx^(n-1)
The point or place where something begins, arises, or is derived.
the function F is said to have a relative maximum at the point c if f(c) > f(x) for all x in an open interval containing c.
a function that is a reverse of another function. Ex: f-1(x)
If f(x)<g(x)<h(x) when x is near a (except possibly at a) and lim x_a f(x)= lim x_a h(x) = L then lim x_a g(x)=L
Implied though not plainly expressed.
The action or process of differentiating.
If f and g are both differentiable and F= f*g is the composite function defined by F(x)= f(g(x)), then F is differentiable and F’ is given by the product
Condition 1: f is continuous on [a,b] Condition 2: f is differentiable on (a,b) Conclusion: f’(x)= f(b)-f(a) / (b-a)
on the curve y=f(x) at the point P(a,f(a)) is the line through P with the slope m=lim x_a (f(x)-f(a))/ (x-a) provided that this limit exists.
Condition 1: f is continuous on the closed interval [a,b] Condition 2: f is differentiable on the open interval (a,b) Conclusion: if f(a)=f(b), then there is at least one number c in (a,b) such that f’(c)=0
If f and g are differentiable, then d/dx[f(x)/g(x)] = (g(x)(d/dx)[f(x)] - f(x)(d/dx)[g(x)]) / [g(x)]^2
implied though not plainly expressed.
the branch of mathematics that deals with the finding and properties of derivatives and integrals of functions.