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Chapter 14: Q. 34 (page 906)

In Problems33鈥�35, find the derivative of each function at the number indicated
34.f(x)=x2鈭�3xat0

Short Answer

Expert verified

The derivative of f(x)=x2-3xat 0 isf'(0)=-3.

Step by step solution

01

Step 1. Find f(0)

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)=x2-3xand 0

Now we have to find, therefore substitute c=0in f(x)to findf(0).

f(x)=x2鈭�3xf(0)=(0)2鈭�3(0)=0

02

Step 2. Use the derivative formula

Substituting all the values in the derivative formula we get,

f鈥�(0)=limx鈫�0f(x)鈭�f(0)x鈭�(0)=limx鈫�0x2鈭�3x鈭�0x=limx鈫�0x2鈭�3xx=limx鈫�0x(x鈭�3)x

=limx鈫�0(x鈭�3)=0鈭�3=鈭�3

Hence the derivative of f(x)whenc=0isf'(0)=-3.

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