**Math 20A Calculus 1 Exam #3 Help**

Show all work and use correct notation. Give exact values unless an approximation is specified. Questions missing relevant work, using incorrect notation, or using only approximations will not receive full credit.

- Find the absolute minimum and absolute maximum values of the function ( ) 2cosf x x x= − on the interval [ ]0,2π (10 points)
- Find the value c guaranteed by the Mean Value Theorem for the function 3( ) xf x x −= on the interval [ ]2,5 . (10 points)
- Consider this function. (20 points)

l( n) x

f x x= .

- On which interval(s) is the function increasing? Decreasing?
- Find any local minimum or local maximum values. Use the First or Second Derivative Tests to prove that the identified point really is a local maximum or minimum.
- On which intervals is the graph concave upward? Downward?
- Find any inflection points of the graph. Explain or show how you know that the identified point is an inflection point. If there is no inflection point, explain why.

## Math 20A Calculus 1 Exam #3 Help

- Consider the graph of this function. (25 points)

2 9 5

( )g x x x

= − −

- Find any x- or y-intercepts of the graph.
- Identify any vertical, horizontal, or slant asymptotes of the graph.
- Identify the intervals where the function is increasing or decreasing.
- Identify any local extreme values. Use the appropriate test to show whether they are maxima or minima.
- Identify the intervals where the function is concave upward and concave downward.

Math 20A Calculus 1 Exam #3

- Find 2

0 lim

cos 1x x x→ −

(5 points)

- Suppose that ‘( ) 6x xf x e += and (0) 0f = . Find the function ( )f x . (5 points)
- Write an expression in sigma notation for the area under the curve siny x= between 0 and π . (5 points)
- Estimate the area under the curve 2 1y x= + between 0x = and 8x = using a left Riemann Sum with 4 intervals. Will this be an overestimate or an underestimate? Explain. (10 points)
- Find the exact value of the definite integral. ( )24 4

162 dxx −

−+∫ (10 points)

MATH 221 FIRST SEMESTER CALCULUS