Given the function f(x)=6+4x^2 calculate the following value:
f(a+h)
I will need help on this problem too!!! :(
see your earlier posting
To calculate the value of f(a+h), we need to substitute the expression a+h into the function f(x) and simplify the expression. Here's how you can do it step by step:
1. Start with the given function: f(x) = 6 + 4x^2.
2. Replace x with (a+h) in the function: f(a+h) = 6 + 4(a+h)^2.
3. Expand the expression (a+h)^2 by multiplying it with itself: (a+h)^2 = (a+h)(a+h) = a^2 + 2ah + h^2.
4. Substitute the expanded expression into f(a+h): f(a+h) = 6 + 4(a^2 + 2ah + h^2).
5. Distribute the 4 over the terms inside the parentheses: f(a+h) = 6 + 4a^2 + 8ah + 4h^2.
6. Combine like terms: f(a+h) = (4a^2 + 8ah + 4h^2) + 6.
7. The final result is: f(a+h) = 4a^2 + 8ah + 4h^2 + 6.
So, the value of f(a+h) is 4a^2 + 8ah + 4h^2 + 6.