   Chapter 9.8, Problem 22E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# In Problems 13-24, find the indicated derivative.Find y ( 5 )  if  d 2 y d x 2 = 3 x + 2 3

To determine

To calculate: The value of y(5) if the second derivative for the function is d2ydx2=3x+23.

Explanation

Given Information:

The provided second derivative for the function is d2ydx2=3x+23.

Formula used:

According to the power rule, if f(x)=xn, then,

f(x)=nxn1

According to the property of differentiation, if a function is of the form, g(x)=cf(x), then,

g(x)=cf(x)

According to the property of differentiation, if a function is of the form f(x)=u(x)+v(x), then,

f(x)=u(x)+v(x)

The derivative of a constant value, k, is

ddx(k)=0

According to the chain rule of derivatives, if there is a function of form y=f(u(x)), then its derivative is

dydx=f(u(x))u(x)

Calculation:

Consider the provided second derivative for the function,

d2ydx2=3x+23=(3x+2)13

To get the value of y(3), differentiate both sides of d2ydx2 with respect to x,

y(3)=ddx((3x+2)13)

Apply the chain rule of derivatives,

y(3)=13(3x+2)131(ddx(3x+2))=13(3x+2)23(ddx(3x)+ddx(2))=13(3x+2)23(3x11+0)=(3x+2)23

To get the value of y(4), differentiate both sides of y(3) with respect to x,

y

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