Question

f(x+h)-f(x)The expressionfor h 70 is called the difference quotient. Find and simplify the difference quotient for the following function.hf(x) = 4x2 + 9x +4The difference quotient is(Simplify your answer.)

Answer 1

we have the function

f(x)= 4x2 + 9x +4

so

step 1

Find f(x+h)

f(x+h)=4(x+h)^2+9(x+h)+4

f(x+h)=4(x^2+2xh+h^2)+9x+9h+4

f(x+h)=4x^2+8xh+4h^2+9x+9h+4

step 2

Find {f(x+h)-f(x)}/h

substitute

{f(x+h)-f(x)}/h={4x^2+8xh+4h^2+9x+9h+4-4x^2-9x-4}/h

simplify

{f(x+h)-f(x)}/h={8xh+4h^2+9h}/h

simplify h

{f(x+h)-f(x)}/h=8x+4h+9

therefore

the answer is

8x+4h+9