f(x)= x + 3. Find and simplify :
f(a+h)−f(a) h
the x +3 is under a radical sign as well! so its the square root of x +3
2 answers
its also / h!
So we have f(x) = √(x+3)
and I bet it is also : (f(a+h)−f(a))/h
(f(a+h)−f(a))/h
= ( √(a+h + 3) - √(a+3) )/h
= ( √(a+h + 3) - √(a+3) )/h * (√(a+h + 3) + √(a+3) ) / (√(a+h + 3) + √(a+3) )
= (a+h+3 - a-3)/( h(√(a+h + 3) + √(a+3) ))
= h/( h(√(a+h + 3) + √(a+3) )
= 1/(√(a+h + 3) + √(a+3) ) , h ≠ 0
and I bet it is also : (f(a+h)−f(a))/h
(f(a+h)−f(a))/h
= ( √(a+h + 3) - √(a+3) )/h
= ( √(a+h + 3) - √(a+3) )/h * (√(a+h + 3) + √(a+3) ) / (√(a+h + 3) + √(a+3) )
= (a+h+3 - a-3)/( h(√(a+h + 3) + √(a+3) ))
= h/( h(√(a+h + 3) + √(a+3) )
= 1/(√(a+h + 3) + √(a+3) ) , h ≠ 0
3 answers