Given function f(x)=-2+4x^2. Find the following

asked Oct 4, 2020 84.3k views

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$f(a) = - 2 + 4 {a}^(2)$

$f(a + h) = - 2 + 4 {(a + h)}^(2) = - 2 + 4 {a}^(2) + 8ah + 4 {h}^(2)$

(f(a + h) - f(a))/(h) = 8a - 4h

Explanation:

$f(a) = - 2 + 4 {a}^(2)$

$f(a + h) = - 2 + 4 {(a + h)}^(2) = - 2 + 4( {a}^(2) + 2ah + {h}^(2) ) = - 2 + 4 {a}^(2) + 8ah + 4 {h}^(2) \\$

$(f(a + h) - f(a))/(h) = \frac{- 2 + 4 {a}^(2) + 2 - 4 {a}^(2) + 8ah - 4 {h}^(2)}{h} = 8a - 4h$

Gregwhitaker answered Oct 10, 2020

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