Use the definition of the derivative to find...?

Question

Use the definition of the derivative to find f(x)= 5x^2 +6x


Thank you s much in advance, an explanation or work would really help!

Geronimo · Accepted Answer

f(x)  =  5x² + 6x

        f(x+h)  =  5(x + h)²  +  6(x + h)

        f(x+h)  =  5(x² + 2xh + h²) + 6x + 6h

        f(x+h)  =  5x² + 10xh + 5h² + 6x + 6h

 f(x+h) – f(x)  =  5x² + 10xh + 5h² + 6x + 6h – (5x² + 6x)

 f(x+h) – f(x)  =  5x² + 10xh + 5h² + 6x + 6h – 5x² – 6x

 f(x+h) – f(x)  =  10xh + 5h² + 6h

 f(x+h) – f(x)  =  h(10x + 5h + 6)

         [ f(x+h) – f(x)  ] ⁄ h  =  h(10x + 5h + 6) ⁄ h

         [ f(x+h) – f(x)  ] ⁄ h  =  10x + 5h + 6


 limit [ f(x+h) – f(x) ] ⁄ h  =  limit 10x + 5h + 6  =  10x + 6  =  f ' (x)
 h→0           h→0

Use the definition of the derivative to find...?

1 Answer