Answer:
(a) k'(0) = f'(0)g(0) + f(0)g'(0)
(b) m'(5) = 
Step-by-step explanation:
(a) Since k(x) is a function of two functions f(x) and g(x) [ k(x)=f(x)g(x) ], so for differentiating k(x) we need to use <u>product rule</u>,i.e., ![\frac{\mathrm{d} [f(x)\times g(x)]}{\mathrm{d} x}=\frac{\mathrm{d} f(x)}{\mathrm{d} x}\times g(x) + f(x)\times\frac{\mathrm{d} g(x)}{\mathrm{d} x}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cmathrm%7Bd%7D%20%5Bf%28x%29%5Ctimes%20g%28x%29%5D%7D%7B%5Cmathrm%7Bd%7D%20x%7D%3D%5Cfrac%7B%5Cmathrm%7Bd%7D%20f%28x%29%7D%7B%5Cmathrm%7Bd%7D%20x%7D%5Ctimes%20g%28x%29%20%2B%20f%28x%29%5Ctimes%5Cfrac%7B%5Cmathrm%7Bd%7D%20g%28x%29%7D%7B%5Cmathrm%7Bd%7D%20x%7D)
this will give <em>k'(x)=f'(x)g(x) + f(x)g'(x)</em>
on substituting the value x=0, we will get the value of k'(0)
{for expressing the value in terms of numbers first we need to know the value of f(0), g(0), f'(0) and g'(0) in terms of numbers}{If f(0)=0 and g(0)=0, and f'(0) and g'(0) exists then k'(0)=0}
(b) m(x) is a function of two functions f(x) and g(x) [ 
]. Since m(x) has a function g(x) in the denominator so we need to use <u>division rule</u> to differentiate m(x). Division rule is as follows : 
this will give <em>
</em>
on substituting the value x=5, we will get the value of m'(5).
{for expressing the value in terms of numbers first we need to know the value of f(5), g(5), f'(5) and g'(5) in terms of numbers}
{NOTE : in m(x), g(x) ≠ 0 for all x in domain to make m(x) defined and even m'(x) }
{ NOTE : 
}
Answer:
3S - F
Step-by-step explanation:
Let Flour be represented with F
Sugar be represented with S
3S = F
3S - F = 0
The correct answers are:
The slope of the line is 4.
A point on the line is (−5, 56)
Step-by-step explanation:
Given equation is:
The slope-intercept form is:
Comparing both equations we get
m = 4
The point is (-5,56)
So, the correct answers are:
The slope of the line is 4.
A point on the line is (−5, 56)
Keywords: Point-slope form, Slope
Learn more about point-slope form at:
#LearnwithBrainly
For a better understanding of the solution provided please go through the diagram in the file attached.
Let ABCD be the rectangular yard. The diagonal d=17 meters. AD=8 meters. Therefore, the length of DC can be found by applying the Pythagorean theorem in the right triangle 
as:
meters.
Answer:
<h2>33</h2>
Step-by-step explanation:
Given the average low temperature by month in Nashville is represented by the function f(x)=-1.4x² + 19x +1.7, where x is the month, the average rate of change is expressed as d[f(x)]/dx = 2(1.4x) + 19
d[f(x)]/dx = 2.8x + 19
Since the number of months between March and August is 5 months and x is in months, hence we will substitute x = 5 into the resulting function to get the average rate of change from March to August as shown;
d[f(x)]/dx at x = 5
= 2.8(5)+ 19
= 14 + 19
= 33
<em>Hence the average rate of change from March to August is 33</em>
