Given f(x)=3x²-5x-2
a) To find f(a+h) replace x with a+h in the given function. So,
f(a+h)=3(a+h)²-5(a+h)-2
=3(a²+2ah+h²)-5(a+h)-2 By using the formula (x+y)²=x²+2xy+y².
=3a²+6ah+3h²-5a-5h-2 By distributing property.
b) Similarly to find f(a) we need to replace x with a. So,
f(a)=3a²-5a-2
So, f(a+h)-f(h)= (3a²+6ah+3h²-5a-5h-2)-(3a²-5a-2)
=3a²+6ah+3h²-5a-5h-2-3a²+5a+2.
=6ah+3h^2-5h (All other terms has been cancel out)
Answer: f is sometimes positive and negative
Step-by-step explanation:
