Final answer:
The quotient (f(10+h)−f(10))/h can be simplified to 5h+154/h, with a=5 and b=154.
Step-by-step explanation:
To find the quotient (f(10+h)−f(10))/h, we need to substitute the given function f(x) = 5x²−6x+10 into the expression. Let's start by finding f(10+h) and f(10).
f(10+h) = 5(10+h)²−6(10+h)+10 = 5(100+20h+h²)−60−6h+10 = 500+100h+5h²−60−6h+10 = 510+94h+5h²
f(10) = 5(10)²−6(10)+10 = 5(100)−60+10 = 500−60+10 = 450
Now, substitute these values into the expression:
(f(10+h)−f(10))/h = (510+94h+5h²−450)/h = (5h²+94h+60)/h = 5h+94+60/h = 5h+154/h
Therefore, the quotient (f(10+h)−f(10))/h can be simplified to 5h+154/h. The values of a and b are a=5 and b=154.
Learn more about Simplifying expressions