f(x) = x^2 -5
Find f(3)
This means find x when it is 3 so just substitute 3 for x
f(3) = 3^2 -5
= 9 - 5
f(3) = 4
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 ).
Car: distancec = 105 km + (90 km/hr)(3 hrs)
Cycle: distancem = ratem(3 hrs)
Equate these 2 distances: 105 km + 270 km = ratem(3 hrs)
Then 375 km / 3 hrs = ratem = 125 km/hr (average speed of the motorcyclist)
<span>let's analyze two cases
</span>
case A) <span>2(√x)−4=10
2</span>√x=10+4----> 2√x=14----> √x=14/2----> square---> x=7²----> x=49
case B)
2√(x-4)=10
√(x-4)=10/2-----> square---> x-4=5²----> x=25+4-----> x=29
The answer is 14 if you're just wanting to divide 84 by 6