Find f(x+h)-f(x)/h for the given function. f(x)=5x^2-6x+4

Question

The correct answer is 10x+5h-6 but how do you get this

Answer 1

The original expression should read f(x+h)/h -f(x)/h. The h in the denominator is for both functions shown. Now set up the following:

5(x+h)² - 6(x+h) +4 - (5x² -6x +4) (I used underline rather than

h h h h h h / for division for clarity)

Multiply the parentheses by the coefficients after expanding the

(x + h)² term. Some h's will cancel from numerator to denominator.

Some terms cancel each other, and you will be left with the correct answer. I leave the rest for you as it is messy to type.

Answer 2

I assume you mean [f(x+h)-f(x)]/h.

Substituting x+h and x into this equation gives:

[5x^2+10xh+5h^2-6x-6h+4-(5x^2-6x+4)]/h

5x^2-6x+4 cancels out of the numerator, leaving

[10xh+5h^2-6h]/h

and dividing by h gives

10x+5h-6

Answer 3