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Use the definition of the derivative to find the derivatives described in Exercises 55-58.

Givenf(3)(x)=3x2+1findd4fdx4andd4fdx42

Short Answer

Expert verified

The value is12

Step by step solution

01

Step 1. Given information

Given functionf(3)(x)=3x2+1

02

Use the definition of derivative and calculate

Calculating, we get

limzxf(3)(z)-f(3)(x)z-x=limzx3z2+1-3x2+1z-xlimzxf(3)(z)-f(3)(x)z-x=limzx3z2-x2z-x=limzx3(z-x)(z+x)z-x=limzx3(z+x)=3(x+x)=6x

d4fdx4x=2=6(2)d4fdx4x=2=12

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