find the difference quotient: f(x+h)-f(x)/h 1. f(x)=-3x+1 2. f(x)=2x^2-x-1

Answer 1

f(x)=-3x+1

Using this function, plug everything into the difference quotient formula

[-3(x+h)+1-(-3x+1)]/h Simplify using the distributive property

[-3x-3h+1+3x-1]/h Simplify by combining like terms

-3h/h cancel out the h's

-3

f(x) = 2x²-x-1

Using this function, plug everything into the difference quotient formula

[2(x+h)²-(x+h)-1-(2x²-x-1)]/h FOIL and distribute

[2(x²+2xh+h²)-x-h-1-2x²+x+1]/h Distribute the last set of parenthesis from the FOILed part

[2x²+4xh+2h²-x-h-1-2x²+x+1]/h Simplify by combining like terms

[4xh+2h²-h]/h Factor an h from the numerator

[h(4x+2h-1)]/h cancel out the h's

4x+2h-1