Horrible wording but I'll say 0 squared and 1 squared
The 87th term of the arithmetic sequence 12, 0, -12 is -1020. The ratio being -12 and the first term being 12.
The Mean Value Theorem:
If a function is continuous on [ a, b ] and differentiable on ( a , b ) than there is a point c in ( a, b ) such that:
f ` ( c )= ( f ( b ) - f ( a ) ) / ( b - a )
f ` ( c ) = ( f ( 2 ) - f ( 0 ) ) / ( 2 - 0 )
f `( x ) = 10 x - 3
f ` ( c ) = 10 c - 3
2 f ` ( c ) = 16 - 2
f ` ( c ) = 7
7 = 10 c - 3
c = 1
Answer:
Yes, the function is continuous on [ 0, 2 ] and differentiable on ( 0, 2 ).
<span>Simplifying
5x + -7 = -10x + 8
Reorder the terms:
-7 + 5x = -10x + 8
Reorder the terms:
-7 + 5x = 8 + -10x
Solving
-7 + 5x = 8 + -10x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '10x' to each side of the equation.
-7 + 5x + 10x = 8 + -10x + 10x
Combine like terms: 5x + 10x = 15x
-7 + 15x = 8 + -10x + 10x
Combine like terms: -10x + 10x = 0
-7 + 15x = 8 + 0
-7 + 15x = 8
Add '7' to each side of the equation.
-7 + 7 + 15x = 8 + 7
Combine like terms: -7 + 7 = 0
0 + 15x = 8 + 7
15x = 8 + 7
Combine like terms: 8 + 7 = 15
15x = 15
Divide each side by '15'.
x = 1
Simplifying
x = 1
</span>
For every f(x) change the x with the given value.
a.
x³-5x²+6x-4 ..........change the x with 2
(2)³-5(2)²+6(2)-4
8-20+12-4
-4
b.
4x³+3x²+x+2 .... .same here change x to 1
4(1)³+3(1)²+(1)+2
4+3+1+2
10
c.
2x^4-x³+3x²-1 ...........change x as -1
2-(-1)³+3(-1)²-1
2+1+3-1
5
d.
2x³-6x-5 ................change x with -3
2(-3)³-6(-3)-5
2(-27)+18-5
-41