Question

Find and simplify a) f(a), b) f(a + h) and c) f(a+h)-f(a) / (h), h≠0 using the given function.

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

Answer 1

Question 22946

$$f(x) = x^2 + 5x - 10$$

1. $f(a) = a^2 + 5a - 10$

2. $f(a + h) = (a + h)^2 + 5(a + h) - 10 = a^2 + 2ah + h^2 + 5a + 5h - 10$

3. $\frac{f(a + h) - f(a)}{h} = \frac{a^2 + 2ah + h^2 + 5a + 5h - 10 - (a^2 + 5a - 10)}{h} = \frac{2ah + h^2 + 5h}{h} = 2a + h + 5$