Calculate Values with a function

Question

Given the function f(x)=4+5x^2, calculate the following values:

f (a)=   

f (a + h)=

f (a + h)- f (a) / h=

Answer 1

Hi Kylie, to solve this problem all you have to do is substitute the values into the function!

For example, you have f(x) = 4 + 5x^2. Then f(a) = 4 + 5(a)^2. Similarly, f(a + h) = 4 + 5(a + h)^2.

So the final expression (f(a+h)-f(a) )/h is equal to (4 + 5(a + h)^2 - ( 4 + 5(a)^2) )/h.

See if you can simplify this a bit more by foiling (a + h)^2 :)

Answer 2

f(a) = 4 + 5a²;

f(a + h) = 4 + 5(a + h)² = 4 + 5a² + 10ah + 5h²;

(f(a + h) - f(a))/h = (10ah + 5h²)/h = 10a + 5h.