The slope is going to be negative. Pick any two points from the graph and find the slope.
m= -3
pick any point on the line, I picked (0,4) and find "b"
y=mx+b
4=(-3)(0) +b
b= 4
y=-3x + 4
Answer:
f is increasing on interval (-infty, 13/4)
Inequality notation: x<13/4
In words: f is increasing on the interval of x that is less than 13/4.
Step-by-step explanation:
f is increasing on interval of x if f' of such interval is positive.
f=-2x^2+13x-8
Differentiate both sides
(f)'=(-2x^2+13x-8)'
Sum and difference rule:
f'=(-2x^2)'+(13x)'-(8)'
Constant multiple rule:
f'=-2(x^2)'+13(x)'-(8)'
Power rule (recall x=x^1):
f'=-2(2x^1)+13(1x^0)-(8)'
Constant rule:
f'=-2(2x^1)+13(1x^0)-(0)
Recall again x^1=x:
f'=-2(2x)+13(1x^0)-(0)
Recall x^0=1:
f'=-2(2x)+13(1×1)-(0)
Associative property of multiplication:
f'=-(2×2)x+13(1×1)-(0)
Performed grouped multiplication:
f'=-(4)x+13(1)-(0)
f'=-4x+13-(0)
Additive identity:
f'=-4x+13
f' is positive when -4x+13>0.
Subtract 13 on both sides:
-4x>-13
Divide both sides by -4:
x<-13/-4
x<13/4
f is increasing on interval (-infty, 13/4)
Given:
where, 
.
To find:
The value of 
.
Solution:
We have,
Differentiate with respect to x.
Using chain rule, we get
Now, put x=5.
![[\because g(5)=-1,g'(5)=8]](https://tex.z-dn.net/?f=%5B%5Cbecause%20g%285%29%3D-1%2Cg%27%285%29%3D8%5D)
![[\because f'(-1)=3]](https://tex.z-dn.net/?f=%5B%5Cbecause%20f%27%28-1%29%3D3%5D)
Therefore, the value of is 24.
Answer:
x = -4/9
Step-by-step explanation:
-3(4x − 2) = 6x + 14
Distribute
-12x+6 = 6x+14
Add 12x to each side
-12x+6+12x = 6x+14+12x
6 = 18x+14
Subtract 14 from each side
6-14 = 18x
-8 =14x
Divide each side by 14
-8/14 = 14x/14
-4/9 = x
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