Write the following expression in exponential form:

Stella [2.4K]

Answer:

The smaller one is x = 3
and the larger one is x = 6

Step-by-step explanation:

A "critical number" is a function argument where the function has zero or undefined slope. A polynomial function never has undefined slope, so we're looking for the x-values where f'(x) = 0.

A graphing calculator easily shows the points that have zero slope. They are found at x = 3 and x = 6.

_____

Setting the derivative to zero is another way to find the points with zero slope:

f'(x) = 6x^2 -54x +108 = 6(x^2 -9x +18) = 6(x-3)(x-6)

The derivative will be zero where the factors are zero, at x=3 and x=6.

The critical numbers are x=3 and x=6.

6 0

2 years ago

Estimate then find the sum 63,824+29,452

ASHA 777 [7]

90,000 becuase 63,824 is rounded down to 60,000 and 29,452 is rounded up to 30,000. 60,000+30,000 is 90,000

3 0

3 years ago

An experiment consist of rolling 3 fair dice (1 red die, a blue die, and a white die) and recording the number rolled on each di

Setler79 [48]

In 1, there are 6 outcomes for each die, so for three dice, the total combination is 6 x 6 x 6 = 216 outcomes. Hence, the probability of any individual outcome is 1/216 

The outcomes that will add up to 6 are
1+1+4 
1+4+1 
4+1+1 
1+2+3 
1+3+2 
2+1+3 
2+3+1 
3+1+2 
3+2+1 
2+2+2 

Hence the probability is 10/216 

In 3, the minimum sum of the three dice is 3. so we start with this
P(n = 3) 
1+1+1 ; 1/216 

P(n = 4) 
1+1+2 
1+2+1 
2+1+1 ; 3/216 

P(n = 5) 
1+1+3 
1+3+1 
3+1+1 
1+2+2 
2+1+2 
2+2+1; 6/216

The sum in 3 is 10/216 or 5/108

3 0

3 years ago

Find f(a), f(a+h), and 71. f(x) = 7x - 3 f(a+h)-f(a) h if h = 0. 72. f(x) = 5x²

Leni [432]

Answer:

$71. \ \ \ f(a) \ = \ 7a \ - \ 3; \ f(a+h) \ = \ 7a \ + \ 7h \ - \ 3; \ \displaystyle\frac{f(a+h) \ - \ f(a)}{h} \ = \ 7$

$72. \ \ \ f(a) \ = \ 5a^{2}; \ f(a+h) \ = \ {5a}^{2} \ + \ 10ah \ + \ {5h}^{2}; \ \displaystyle\frac{f(a+h) \ - \ f(a)}{h} \ = \ 10a \ + \ 5h$

Step-by-step explanation:

In single-variable calculus, the difference quotient is the expression

$\displaystyle\frac{f(x+h) \ - \ f(x)}{h}$ ,

which its name comes from the fact that it is the quotient of the difference of the evaluated values of the function by the difference of its corresponding input values (as shown in the figure below).

This expression looks similar to the method of evaluating the slope of a line. Indeed, the difference quotient provides the slope of a secant line (in blue) that passes through two coordinate points on a curve.

$m \ \ = \ \ \displaystyle\frac{\Delta y}{\Delta x} \ \ = \ \ \displaystyle\frac{rise}{run}$ .

Similarly, the difference quotient is a measure of the average rate of change of the function over an interval. When the limit of the difference quotient is taken as h approaches 0 gives the instantaneous rate of change (rate of change in an instant) or the derivative of the function.

Therefore,

$71. \ \ \ \ \ \displaystyle\frac{f(a \ + \ h) \ - \ f(a)}{h} \ \ = \ \ \displaystyle\frac{(7a \ + \ 7h \ - \ 3) \ - \ (7a \ - \ 3)}{h} \\ \\ \-\hspace{4.25cm} = \ \ \displaystyle\frac{7h}{h} \\ \\ \-\hspace{4.25cm} = \ \ 7$

$72. \ \ \ \ \ \displaystyle\frac{f(a \ + \ h) \ - \ f(a)}{h} \ \ = \ \ \displaystyle\frac{{5(a \ + \ h)}^{2} \ - \ {5(a)}^{2}}{h} \\ \\ \-\hspace{4.25cm} = \ \ \displaystyle\frac{{5a}^{2} \ + \ 10ah \ + \ {5h}^{2} \ - \ {5a}^{2}}{h} \\ \\ \-\hspace{4.25cm} = \ \ \displaystyle\frac{h(10a \ + \ 5h)}{h} \\ \\ \-\hspace{4.25cm} = \ \ 10a \ + \ 5h$

4 0

2 years ago

Consider the given function.

Neporo4naja [7]

The first interception for this function would be at (1,0) the next would be (4,0)

6 0

3 years ago

Read 2 more answers