MATHEMATICS QUESTION

Question

If f(x) = 5x² − x + 9 and h ≠ 0, find the following and simplify.

(a)    f(x + h)

(b)	(f(x + h) − f(x)) / h

Answer 1

5x^2 - x +9

f(x+h) = 5(x+h)^2 - (x+h) + 9==5x^2 + 10xh + 5h^2 -x -h + 9

f(x+h) - f(x) = 5h^2 + 10xh -h

divide by h gives 5h +10x -1

check the answer by taking the derivative of f(x)

f'(x) = 10x -1 which equals 5h+10-1 when h=0