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Chapter 4: Q. 3 (page 364)

Find a function f that has the given derivative f' and value f(c), if possible.

f'(x)=3e2x+1,f(0)=2

Short Answer

Expert verified

Hencethefunctionis3e2x脳2+x-4

The value of f(-4) =3脳e-8-8

Step by step solution

01

Step 1. Given 

The given function isf'(x)=3e2x+1,f(0)=2

02

Step 2. Finding the function using integration 

Integratingfunctionwithrespecttox鈭�f'(x)=鈭�3e2x+1,f(0)=2=鈭�3e2x+1dx=3e2x脳2+x+cwherecisconstantwhenf(0)=2f(0)=3e2*0*2+0+c2=6+cc=-4Hencethefunctionis3e2x脳2+x-4

03

Step 3. Finding the value f(c)

f(x)=3e2x脳2+x-4f(-4)=3脳e2*-4+(-4)-4=3脳e-8-8

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