Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

$$\text { Find } f^{\prime \prime}(x) \text { if: (a) } f(x)=x^{5}+3 x^{2}+5 ; \text { (b) } f(x)=2 x^{4}+3 x^{2}+1$$

(a) $20 x^{3}+6$(b) $24 x^{2}+6$

Calculus 1 / AB

Chapter 3

Applications of the Derivative

Section 3

Concavity and the Second Derivative

Derivatives

Campbell University

Oregon State University

Baylor University

University of Michigan - Ann Arbor

Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

30:01

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (the rate of change of the value of the function). If the derivative of a function at a chosen input value equals a constant value, the function is said to be a constant function. In this case the derivative itself is the constant of the function, and is called the constant of integration.

01:00

find $f^{\prime \prime}(2)…

02:07

Find $f^{\prime \prime}(x)…

01:03

Find $f^{\prime}(x)$$$…

0:00

Find $f^{\prime}(a)$.$…

01:01

01:02

Find $f^{\prime}(x)$.$…

question two is asking you to fine f double prime of X Um For part A for F of X equals X to the fifth plus three x squared plus five. So first taking the first derivative using this formula over here, we can say that it is five x to the forest plus six x now taking the second derivative. That would be 20 x to the third plus six, which is your answer for part A for part B. Then they're asking when F of X is equal to two x to the fourth plus three x squared plus one using that same formula again, if prime of X is equal 28 x to the third plus six x and f double prime of X is equal to 24 x squared plus six and those are answers for Question two.

View More Answers From This Book

Find Another Textbook

01:19

Use the appropriate rules to determine the derivative.$$s=-16 t^{2}+256 …

01:11

Suppose that, in the development of the definition of the derivative, we wro…

01:10

Show that if two functions $f$ and $g$ have the same derivative on the same …

01:30

Let $f(x)=x^{-1 / 2}$ on the interval (0,1] . (a) Does $f$ satisfy the condi…

01:43

Find all the asymptotes and plot the graph of the given function.$$f(x)=…

03:33

Find the points on the curve whose equation is $x^{2}+y^{2}=16$ nearest and …

01:06

$$\text { Find } \frac{d^{2} y}{d x^{2}}, \text { if } 3 x^{2}-2 y^{2}=6$$

01:07

In Example $7,$ find the relationship between $n$ and $x$ in the two methods…

02:01

Find $d v / d t$ if $v=t^{2} \cdot \sqrt[3]{(2 t+8)^{2}}$.

01:48

Locate all critical points.$$h(x)=\left(12-x^{2}\right)^{1 / 2}$$