All AP Calculus AB Resources
Example Questions
Example Question #906 : Ap Calculus Ab
Example Question #907 : Ap Calculus Ab
Example Question #201 : Integrals
Example Question #202 : Integrals
Example Question #21 : Riemann Sums (Left, Right, And Midpoint Evaluation Points)
Example Question #22 : Riemann Sums (Left, Right, And Midpoint Evaluation Points)
Example Question #23 : Riemann Sums (Left, Right, And Midpoint Evaluation Points)
Example Question #24 : Riemann Sums (Left, Right, And Midpoint Evaluation Points)
Example Question #21 : Riemann Sums (Left, Right, And Midpoint Evaluation Points)
Let .
A relative maximum of the graph of can be located at:
The graph of has no relative maximum.
At a relative minimum of the graph
, it will hold that
and
.
First, find . Using the sum rule,
Differentiate the individual terms using the Constant Multiple and Power Rules:
Set this equal to 0:
Either:
, in which case,
; this equation has no real solutions.
has two real solutions,
and
.
Now take the second derivative, again using the sum rule:
Differentiate the individual terms using the Constant Multiple and Power Rules:
Substitute for
:
Therefore, has a relative minimum at
.
Now. substitute for
:
Therefore, has a relative maximum at
.
Example Question #911 : Ap Calculus Ab
Estimate the integral of from 0 to 3 using left-Riemann sum and 6 rectangles. Use
Because our is constant, the left Riemann sum will be
Certified Tutor
Certified Tutor
All AP Calculus AB Resources
