Sea la función LaTeX : f \ left(x \ right) = ax ^ 2 + bx f ( x ) = a x 2 + b x determine LaTeX : Lim_{h \ rightarrow0} \ left[ \ frac{f_{ \ left(x + h \ right)} - f_{ \ left(x \ right)}}{h} \ right] L?

Cuando x = 4, f(4) = 61.

008

Explicación :

a.

Determine

<img src="https://tex.z-dn.net/?f=Lim_%7Bh%5Crightarrow0%7D%5Cleft%5B%5Cfrac%7Bf_%7B%5Cleft%28x%2Bh%5Cright%29%7D-f_%7B%5Cleft%28x%5Cright%29%7D%7D%7Bh%7D%5Cright%5D" />

Ese límite se conoce como función derivada de la función f(x).

En el caso que nos ocupa

<img src="https://tex.z-dn.net/?f=Lim_%7Bh%5Crightarrow0%7D%5Cleft%5B%5Cfrac%7Bf_%7B%5Cleft%28x%2Bh%5Cright%29%7D-f_%7B%5Cleft%28x%5Cright%29%7D%7D%7Bh%7D%5Cright%5D%3DLim_%7Bh%5Crightarrow0%7D%5Cleft%5B%5Cfrac%7B%5B%20a%28x%2Bh%29%5E2%2Bb%28x%2Bh%29%5D-%28%20ax%5E2%2Bbx%29%7D%7Bh%7D%5Cright%5D%20%5Cqquad%20%5CRightarrow" />

<img src="https://tex.z-dn.net/?f=Lim_%7Bh%5Crightarrow0%7D%5Cleft%5B%5Cfrac%7Bf_%7B%5Cleft%28x%2Bh%5Cright%29%7D-f_%7B%5Cleft%28x%5Cright%29%7D%7D%7Bh%7D%5Cright%5D%3DLim_%7Bh%5Crightarrow0%7D%5Cleft%5B%5Cfrac%7B2axh%2Bah%5E2%2Bbh%7D%7Bh%7D%5Cright%5D%20%5Cqquad%20%5CRightarrow" />

<img src="https://tex.z-dn.net/?f=%5Cbold%7BLim_%7Bh%5Crightarrow0%7D%5Cleft%5B%5Cfrac%7Bf_%7B%5Cleft%28x%2Bh%5Cright%29%7D-f_%7B%5Cleft%28x%5Cright%29%7D%7D%7Bh%7D%5Cright%5D%3DLim_%7Bh%5Crightarrow0%7D%5Cleft%5B2ax%2Bah%2Bb%5Cright%5D%3D2ax%2Bb%7D" />

b.

Calcular su valor cuando x = 4 .

( Considere los valores de a = 2.

899 y b = 3.

656 )

Cuando x = 4, f(4) = (2.

899)(4)² + (3.

656)(4) = 61.

008.