Find and simplify a) f(a), b) f(a + h) and c)
F(a+h) - f(a) / h ;
1. f(x) = x^2 + 5x -10
f(a+h) = (a+h)^2 + 5(a+h) - 10
f(a) = a^2 + 5a - 10
(f(a+h)-f(a))/h
= (a^2 + 2ah + h^2 + 5a + 5h - 10 - a^2 - 5a + 10)/h
= (2ah + h^2)/h
= 2a + h
oops
(2ah + 5h + h^2)/h
= 2a + 5
To find and simplify the given expressions involving the function f(x) = x^2 + 5x - 10, follow the steps below:
a) Finding f(a):
To find f(a), substitute the value of a into the function f(x) and simplify:
f(a) = (a)^2 + 5(a) - 10
= a^2 + 5a - 10
So, f(a) = a^2 + 5a - 10.
b) Finding f(a + h):
To find f(a + h), substitute the value of a + h into the function f(x) and simplify:
f(a + h) = (a + h)^2 + 5(a + h) - 10
= (a^2 + 2ah + h^2) + 5a + 5h - 10
= a^2 + 2ah + h^2 + 5a + 5h - 10
So, f(a + h) = a^2 + 2ah + h^2 + 5a + 5h - 10.
c) Finding [F(a + h) - f(a)] / h:
To find [F(a+h) - f(a)] / h, you need to determine F(x) first.
Since F(x) is not defined, it is not possible to evaluate [F(a+h) - f(a)] / h using calculus techniques.
However, you can still evaluate the expression if we have more information about F(x). If you could provide more details about F(x), I can guide you further in evaluating [F(a+h) - f(a)] / h.
Please double-check if there is any additional information or clarification about F(x) that you can provide.