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Chapter 2: Q 28 (page 238)

Find a function fthat has the given derivative f'and value f(c).

f'x=-32x+4,f0=100

Short Answer

Expert verified

Antiderivaivefx=-16x2+4x+100

Step by step solution

01

Step 1:Given information

Given expression isf'x=-32x+4,f(0)=100

02

Step 2:Simplification

given

f'(x)=-32x+4

We will use an intelligent guess-and-check method to find f

here,-32xis derivative of -16x2and 4 is derivaive of 4x

hence,

fx=-16x2+4x+c

now

f0=100,鈬�100=0+c

鈬�c=100

Therefore

f(x)=-16x2+4x+100

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