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Given the function f(x)=-8 + 8 x², calculate the following values: f(a), f(a+h), and (f(a+h) - f(a))/(h).

User LpLrich
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Final answer:

To solve for f(a), f(a+h), and the expression (f(a+h) - f(a))/h, one must substitute the variables into the function f(x) = -8 + 8x² and simplify. The calculations involve basic algebraic manipulation and substitution.

Step-by-step explanation:

The question asks to calculate values of the function f(x) = -8 + 8x² for f(a), f(a+h), and the expression (f(a+h) - f(a))/h. Let's break down the steps for each calculation.

Calculating f(a)

Simply substitute a for x in the function:

f(a) = -8 + 8a²

Calculating f(a+h)

Now substitute (a + h) for x:

f(a+h) = -8 + 8(a+h

= -8 + 8(a² + 2ah + h²)

Calculating the expression (f(a+h) - f(a))/h

Subtract f(a) from f(a+h) and divide by h:

((-8 + 8(a² + 2ah + h²)) - (-8 + 8a²))/h

= (8ah + 8h²)/h

= 8a + 8h

User Enwired
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