Math Homework Need Help

Question

Let f(x)=1/2x²-1. Find slope m_PQ of the secant line that contains points P=(2,f(2)) and Q=(2+h,f(2+h)) and then compute m_PQ for h=0.5.

Answer 1

f(2) = 1/2(2)² - 1 = 1 ; P: (2 , 1)

f(2 + h) = 1/2(2 + h)² - 1 = 1/2h² + 2h + 3 ; Q: (2+h , 1/2h² + 2h + 3)

m_PQ = [ (1/2h² + 2h + 3) - 1] / [ (2+h) - 2 ] = (1/2h² + 2h + 2) / h = 1/2h + 2 + 2/h

m_PQ | _h=.5 = 6.25