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Chapter 14: Q. 35 (page 906)

In Problems33鈥�35, find the derivative of each function at the number indicated.
35.f(x)=2x2+3x+2at 1

Short Answer

Expert verified

The derivative of f(x)=2x2+3x+2at 1 is f'(1)=7.

Step by step solution

01

Step 1. Find f(1)

To find the derivative we have to use the formula,

f鈥�(c)=limx鈫�cf(x)鈭�f(c)x鈭�c

We have been given f(x)=2x2+3x+2andc=1

Now we have to find, therefore substitute c=1in f(x)to find f(1).

f(x)=2x2+3x+2f(1)=2(1)2+3(1)+2=2+3+2=7

02

Step 2. Use the derivative formula

Substituting all the values in the derivative formula we get,

f鈥�(1)=limx鈫�1f(x)鈭�f(1)x鈭�(1)=limx鈫�12x2+3x+2鈭�7x鈭�1=limx鈫�12x2+3x鈭�5x鈭�1=limx鈫�1(2x+5)(x鈭�1)x鈭�1=limx鈫�1(2x+5)=2(1)+5=2+5=7

Hence the derivative of f(x)when c=1is f'(1)=7.

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