Question
Asked Apr 8, 2019
11 views
Let
2x2 +7x +13
r+1
12+5
+1
(a) Find f(x) and f"(x).
(b) Use f(x) to identify critical numbers and use the second derivative test to determine the
local maximum and local minimum
(c) Determine intervals of increase and decrease and
(d) Intervals of concavity and inflection points, if any.
(e) Sketch the graph of f(x). What line is the slant asymptote? What line is the vertical asymp-
tote and why? Show them on the graph
help_outline

Image Transcriptionclose

Let 2x2 +7x +13 r+1 12+5 +1 (a) Find f(x) and f"(x). (b) Use f(x) to identify critical numbers and use the second derivative test to determine the local maximum and local minimum (c) Determine intervals of increase and decrease and (d) Intervals of concavity and inflection points, if any. (e) Sketch the graph of f(x). What line is the slant asymptote? What line is the vertical asymp- tote and why? Show them on the graph

fullscreen
check_circle

Expert Answer

Step 1

We use the power rule of differentiation which is derivative if x^n is nx^(n-1)  to find f'(x) and f''(x).

fullscreen
Step 2

2) We now that the critical numbers are the solutions of f'(x)=0, so we set f'(x)=0 and find the value of satisfyingf'(x)=0

Therefore, critical numbers are 1 and -3.

fullscreen
Step 3

Since, at x=1, f''(x)>0, and at x=-3, f''(x)<0

Therrefore, ...

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Calculus

Derivative

Related Calculus Q&A

Find answers to questions asked by student like you
Show more Q&A
add
question_answer

Q: Evaluate the following integral as written. Please refer to attached image.

A: It's  aquestion of double integral. We will first evalaute the integral with respect to x, put the l...

question_answer

Q: how do i get number 3

A: Expanded the expression of f(x) first then used the exponent rule to find the derivatives. 

question_answer

Q: The beginning of the question is attached.  How do I argue that f(x) is concave if and only if g(x)=...

A: A function is concave or ceonvex is defined by the sign of its double derivative.A function is conve...

question_answer

Q: 21 If fx)3then f(x) O 2x-2-1 3x 2x-3r2-3 3x O 2x-3x2-3 6x 2x 3x+2 O 2x-x2-1

A: Find the derivative of the given function.

question_answer

Q: Evaluate the integral in cylindrical coordinates. Please see attached image.

A: To calculate the value of the integral in cylindrical coordinates which is shown below,

question_answer

Q: Need solution to 1b.

A: Part 1b.In this question, we have a function for which we have to solve limits, function is given be...

question_answer

Q: The DeWitt Company has found that the rate of change of its average cost for product is C'(x)=(1/4)-...

A: Given information:The DeWitt Company has found that the rate of change of its average cost for produ...

question_answer

Q: Use the shell method to find the volume of the solid generated by revolving the region bounded by x ...

A: We are given equations as 

question_answer

Q: b. Find the area of the region bounded by Y = xe ax and the x-axis on the interval 0,41, where a> 0....

A: Area of region which is bounded by f(x) and x-axis on [0,4] computed as follows.