For the function fx x2 x 1 determine the following f34 Sim

For the function f(x) =x^2 + x - 1 determine the following f(3/4) (Simplify your answer completely): Find the difference quotient for the function g(x) = 5x^2 + 7x - 10 and simplify it. 10x + 5h + 7 10x - h + 7 10x^2 + 5h^2 + 7h 10x + 7

Solution

f(x) = x^2 + x -1

f(3/4) = (3/4)^2 + (3/4) - 1

= 9/16 + 3/4 -1

= (9 + 12 -16)/16

= ( 5/16)

g(x) = 5x^2 + 7x- 10

g(x+h) = 5(x+h)^2 + 7(x+h) - 10

= 5x^2 + 5h^2 + 10xh + 7x +7h -10

difference quotient = [ g(x+h) - g(x) ]/ h

= [ 5x^2 + 5h^2 + 10xh + 7x +7h -10 - 5x^2 - 7x +10]/h

= 10x +5h + 7