   Chapter 9.8, Problem 38E ### 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

# Photosynthesis The amount of photosynthesis that takes place in a certain plant depends on the intensity of light x according to the equation f ( x ) = 145 x 2 − 30 x 3 (a) Find the rate of change of photosynthesis with respect to the intensity.(b) What is the rate of change when x =   1 ? When x =   3 ?(c) How fast is the rate found in part (a) changing when x =   1 ? When x =   3 ?

(a)

To determine

To calculate: The rate of change of the photosynthesis, where the amount of the photosynthesis that takes place in a certain plant is represented by the function, f(x)=145x230x3.

Explanation

Given Information:

The amount of the photosynthesis that takes place in a certain plant is represented by the function, f(x)=145x230x3, where x represents the intensity of light.

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

Calculation:

Consider the provided cost function,

f(x)=145x230x3

To find the rate of change of photosynthesis, differentiate the profit function with respect to x,

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(b)

To determine

To calculate: The rate of change of the photosynthesis, where the amount of the photosynthesis that takes place in a certain plant is represented by the function, f(x)=145x230x3, when x=1 and when x=3.

(c)

To determine

To calculate: The rate at which rate of change of the photosynthesis, where the amount of the photosynthesis that takes place in a certain plant is represented by the function, f(x)=145x230x3, changes when x=1 and when x=3.

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