Calculus Answers

Determine whether f is 1-1 by examining sign of f'(x)
f(x)= x/x+1

∫102e8x−4e4xdx=

Evaluate the definite integral:
∫−4−7(x−1+3x)dx=

Consider the function f(x)=−2x3+45x2−300x+5. For this function there are three important intervals: (−∞,A], [A,B], and [B,∞) where A and B are the critical values.
Find A

and B

For each of the following intervals, tell whether f(x) is increasing (type in INC) or decreasing (type in DEC).
(−∞,A]:

[A,B]:

[B,∞)

f(x) has an inflection point at x=C
where C is

Finally for each of the following intervals, tell whether f(x) is concave up (type in CU) or concave down (type in CD).
(−∞,C]:

[C,∞)

Suppose that
f(x)=x3−6x2+10.
(A) List the x values of all local maxima of f. If there are no local maxima, enter 'NONE'.
x values of local maximums =
(B) List the x values of all local minima of f. If there are no local minima, enter 'NONE'.
x values of local minimums =
(C) List the x values of all the inflection points of f. If there are no inflection points, enter 'NONE'.
x values of inflection points =

Answer the following True-False quiz. (Enter "T" or "F".)
1. A continuous function on a closed interval always attains a maximum and a minimum value.
2. Continuous functions are always differentiable.
3. If f′(c)=0 and f′′(c)>0, then f(x) has a local minimum at c.
4. If f(x)=e2, then f′(x)=2e.
5. If f(x) and g(x) are increasing on an interval I, then f(x)g(x) is increasing on I.
6. If a function has a local maximum at c, then f′(c) exists and is equal to 0.
7. Differentiable functions are always continuous.

Evaluate ∫20f(x)dx, where
f(x)={7x6,2x4,0≤x<11≤x≤2.


∫20f(x)dx =

Evaluate the definite integral
∫728x−−√dx

∫2bbx5dx =